{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Programming Exercise 3Programming Exercise 3\n",
    "## Multi-class Classiﬁcation Multi-class Classiﬁcation "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import minimize\n",
    "from scipy.io import loadmat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((5000, 400), (5000, 1))"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = loadmat('./ex3data1.mat')\n",
    "# image = data['X'][1].reshape(20,20)\n",
    "# plt.matshow(image,cmap='gray_r')\n",
    "data['X'].shape,data['y'].shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_100_image(X):\n",
    "    sample_index = np.random.choice(X.shape[0],100) #从 N（个样本）中，随机选出100个数字\n",
    "    sample_images = X[sample_index,:]#选择其中随机的100行 (100,400)\n",
    "    \n",
    "    fig, ax_arraya = plt.subplots(nrows=10,ncols=10,sharex=True,sharey=True,figsize=(8,8))\n",
    "    for row in range(10):\n",
    "        for col in range(10):\n",
    "            ax_arraya[row,col].matshow(sample_images[10*row + col].reshape(20,20), cmap = 'gray_r')\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UODRkyBDA53Q196lFVOlCeTRFFPTiA9UQ6HyWLVvm7EaevMr8tSVMm/aljIqLiyMbu67zd999x/333w94+9Acq1BJdQjDhw93tiSiiOjUFJ37kCFDXLThhhtuAHyx1e233w4k6x4geX+p7kA2qxZ+Um4qblJBUWrBXxQRCY17iy22cFEq5caVn5d9a62eNWuWsyGtO/qZzjX4co3i4uLIC8gKCwudyr/tttsAnBLVfaXz++OPP1xUUJE22a5Uf5CysjJXrKexq7VfdZjyNAzDMIyQRNZXS09slcer0bRyKfJg9tprLxdbl9crDy6K7SdhkOcrr1CenpRM//79Adhzzz3Zc889Kz2GfleeWaaaZEvBaF7HjBkD+Dncf//9nUcsdaqtFvLEolZsZWVlrFixwuWBBw8eDCTnRJ9VlWpJrd5TFaeaE2gD/wMPPFDuPKSS0qXiNLeqppTaV8WkcvIXX3yxy7tp7FJ3QZtK9yuxSktLXcRBuR1VnepeTK1OVpQg2PBA94bGnw51J5U5fvx4Ro0aBZRXuOCbdShnvNFGG6U1t7kyUl8jp8p2fQ2Ses0155tvvjlQUU3quKm2HKWCS91qo+iZtgIqj6jcZ+rn6rrr79UWT19VD/DKK68AychL1MozkUi4ZiOqo1D0TDsGZOM77rijm2NVK6tBRlX2klrN26ZNG6Bm96kpT8MwDMMISWTKM/jya+VK5JGnVmelM99TUxKJhBvTwQcfDPi9VzoH5SFyc3MzroorI5FIuDylqsLUiFwVoMrFXnbZZa6iVa20VJ0aVZVkZaS+6q02G6azs7Ndfllt8E466aRyx1NOWueVLnvS/EiN6fOlypQX6dy5s7MljUWecKZf/F5UVOQiKbr+48ePLzc2NVHo3Lmziw4opyiPOxN5REVrdtttN1cZ+fPPPwNw4IEHAr65il5Hl8n8ZnUkEoka1wrEYjFnS+l4gUEYSkpK3NqsPaWqvldDfbH//vs7JaZq4alTpwJ+b62uixrC7LzzzhXarkaB7j3dV9qhobytyM/Pdypfc62/rW48waYPVm1rGIZhGGkgbe8SClaK1RfPK5VgnkGeupAXXh9UZxC1tVPus1evXgBOtUHFauX6oPhXRklJiTsHNaXWnmHtS5VaSrct6fqrglbVqkK2XZkayrTiFKlVwlLGqj8QOq/s7OwKe3wzmUfU9evUqZOLJuh7ynFF2X3JSKK5VG5Q+9m1312N7bfYYgu3Y0B5Q73+TV2JtCNBEbF1113XRWbSaUs6B/UREIWFhRmzYVOehmEYhhGStL/FdlVUxNWW+qSKq0IxefXYVAeWYK/bhkpqn2RV0qnScmUVu1ETzIM0FIIdrYIqWMo0kUjUixxi6osXgvsKjfSh+0gVzurYlPr6MilOVWNrf6W6+AhFZ/r16+eiBumuLM/UZ1RFZl8Bb0SGDHx1XmR0c1vIrm40BAe2IYxxdaWybTLBnwmlVIKNKlLXo1X5QMskFrY1DMMwjJCY8jQMwzBqhCJdq3PEq6aY8jQMwzCMkNjD0zAMwzBCYg9PwzAMwwhJLEyVWywWmwf8lr7h1IpOiUSiTVU/tDFHRrVjhoY57oY4ZmiY47YxR4bZR+aocsyhHp6GYRiGYVjY1jAMwzBCYw9PwzAMwwiJPTwNwzAMIyT28DQMwzCMkNjD0zAMwzBCYg9PwzAMwwhJqN62+fn5iYKCgnSNpVZMnDhxfnV7h/Ly8hKdOnXK5JBWysrG3BDnGRrmuBvimKFhjrshjrkhrh+QHHd9m+tJkyatdK47duyYySGtlMmTJ1c55lAPz4KCAj788MNoRhURzZs3r3ZTbadOnfjggw8yNZwa0aJFi2rHXFBQwEcffZSp4dSIZs2arXTzckO0j4Y4ZmiY426IY26I6wck53rs2LGZGE6Nad26dbXj7tixY70bc15eXpVjtrCtYRiGYYTEXklm1Huys5NmmpWVBfgX78ZiMSD5Et+ysrJVM7h/GfF43M2/dScz/s2Y8jQMwzCMkGRMeQbVAiS92FRMPRjxeNwpTNnHzz//DMDbb78NwMKFCwHYcMMNAdhmm23Iy8sDzIbShe7bxYsX06RJEwBycnKA9CpQ2YA+v6ysbLVUvKnrolhV55k6ltVxrqMibQ/P4MMyNzcXgJKSEvezn376CfA34TrrrAP48JwWwkQiUalxGQ2foH1Mnz6dH374AYBJkyYBMHr0aAC++eYbIBmmBVhzzTUBOOKII7jsssuAzCzoDQXdR6n3Hvj5C0Pjxo0BeOCBB2jbti0A++67b7njpoNZs2YBMH/+fAC6devmHt6lpaVA5Q+e+kRWVpa7FpqroJMnJ6GoqAhIXrPU9S+daP4aNWoE+HktLi521102o5/VN3QOWVlZFRwuzXnUY7ewrWEYhmGEJG3KU099eQG//PILAE888YQLw3377beA92o7d+4MQJ8+fQA46qijyh0r3aR6L+ALVWKxmPMIa+q9xGIx9/f6m39rSDF1LuTBBufm9ddfB+Dqq6/m+++/B7wXvu666wJw0EEHAbDeeusBcN999wHw/vvvc/rppwOw1lprlTvuvxHdc3/99RcAX375JZDcvgBJ9Qbh7FHH/PPPP3nrrbcArzyjRPfe1KlTAb8G/P7770AyRH/XXXcBuFB9fY0yyMYXL17MzJkzAejQoQMAzZo1A/yao2s0fPhwAAYMGMDhhx9e7jhRrx/B444fPx6Ar7/+GkhGfgYNGgRAr169AGjdujWw6u8vzZuiEP/88w+QtE9FKWQXmnPZS1RjN+VpGIZhGCGJXHnqaa88y+effw7A0KFDAZg2bZr7HXmZ8iImT54MJJUEwKGHHgpA06ZN0+pdBpWtcrEff/wxkFRA/fv3B5IbeaFq70UeeklJCRMnTgS8x5+fn1+ncYWdA/19qoJOPY7+r3OJPCfw/3OxfPlyXnzxRQBatmwJwCabbALgVMRjjz0GwLJly9h2220B6N27NwD7778/kFQdACtWrADgiy++AJKqdfHixQC0a9cuLedSWzQHlRW+pCOnFYvF3GfccsstANx4440AnHnmmQBce+21bgxhicfjfPfdd1EMtVKkJNRMQflvzdF7773HU089BcC5554LeNVRWFgI+Ly3vpaVlWXUHhRJmzJlCpCc7wkTJgBw0kknlfuqNXDOnDmAXy8nTpxIv379AB95iUp5aj2YPXs24O3kwQcfBPza3bNnTw488EAArrzySsCv45nKxwrdP5ovXet7770XwM3v1KlT+eOPPwC/Buywww4AXH/99YBfh+s6n6Y8DcMwDCMkkSnPoJqUZ3DHHXcAPo7erFkz50UEvRd5PJnahB3MccrrO+GEEwDvDZaVlbmKT+XZWrVqBXjvRmPXOb366qucddZZABx99NEAXHPNNaHGF2wOUFxcXGMPOh6PO4/81VdfLXd+n332GQDbb789AIMHDwaSSi/KykmN/80333S5nCFDhgAwatQowCuMDTbYAEhWzh5yyCGAz1/q/JctWwZUrFjMysqqoKpXNTp33Qeac9nP8uXL2WmnnQA45ZRTgGjUcjweZ/r06YD3yjXnZ5xxRujP0bzKlmbNmuW+F2UtgtTauHHjgGRVL/hrrMrqpUuX8t577wHefu+8807Aq4/27dsDuPkdNGhQrfK8NSW4jqi+Q3n4999/v0JuU9GTpk2blhtr165dgWS+UTn/qMeqcT7xxBOAnz9FdhSZ6N69OxdddBGQvIcB/vOf/wD+emRC0cfjcXfdPv30U8CrSEX3tthiCyC5fih68dtvyc56Dz30EICLmOy5556AvwalpaW1WjdMeRqGYRhGSGqlPIM5s1gs5pSXPFTFyF966SUAWrRoASSr53r06AH4asBHH30U8LnGTCEPTB7KeeedB8CiRYsA7928/fbbzqv9888/AWjTJtloX3Mgb195g/vvv9/9bP311wfCVerm5OQ4L1we0yGHHOKq3VS1WpVKz8rKclWRylPII9f8v/HGG4BX2I8//ngkylORhSVLlgDJfZpqbKDcp6oPVU154oknAsmqvmB1ss41qC4ry7usij1/qdXEyrM9++yzAC4/p0pGVS0OGDCAPfbYA4hWLWdlZTlPW/v2jjzySMDvo9Y9mtqQQmPQ3Ov/upbKKf/5559E/ZaReDzOyy+/DPh1Y9q0aQBsttlmgFfNI0aMcOpDlaCyLakhVVvq5QpPPfUU55xzDuCVUxSKKag4NVdaA3Tf7rTTTm7MNT1msIFMVMTjcbdfWrlw5VYfeeQRwNcl5OTkuJynokGyA61D1Sn5utp1ak2G8rKKpmgNU81E3759AWjevLm7HqqdUT2FnjdfffUV4PPra6+9trt/w4zZlKdhGIZhhKRWyjPYxWXOnDkV8iyKket3Ff8/44wznGcjD1hVaTpGOnIqlRGsCJYCVV5q7733BpJ5OVW8bbzxxoD3uKTuLr30UsB3wWnfvj0jRowAfIxd+a+VIeWpYyl3+uKLLzJgwAAA9ttvP8B7gJU1T//kk08A70nKA1P+59ZbbwWosVdcU3TddL7z589335sxYwbgVbA6A2kvlvIQlSF7k03pPD7++ONaeY61JVj5V1RU5FoHPv3004DviiS1pzySbKFdu3buXKPIw2ksCxYscDlBeefKB+l6aK7mzp3rIioaZ8+ePQGfg9RxFXGZO3euU891RfffuHHjnDJURyHNiSrutcf36aefdveF5k85XdUWKHqieovnnnvORbf0u3UlFos59Sr1ozVC64YiTttvv737nnKeiryo6vzHH38EcJWirVu3dvMTJbm5ua7eQPek5ljrRGrVsuZYNqTuUsFuRPqb1G5KsrPaRrNkg88//zw33XQT4BWwaigUbUitg5AN3XbbbYC3qeuuu67cmHUuV199NZtvvjlAqDxz6IdnIpFwG5YVlrjyyivdpmZNnAxn4MCBgA+JlpaWugHKgLQlRAufLkQ6F8Ls7GxXrKLQskJra6+9NkC5xgi777474Mu7hw0bBsAzzzwDeGNS8ceJJ55I9+7dgapbclVFWVkZK1ascIYiA37qqafcPF511VWAN3gl+/UQisfjbuuPjPiFF14A/EL45JNPAn4rSFSk9kGFpEMhu9A8yQlo3rw5EM5odSxdp+bNm7sHajoIti9bvnw5kFyUIelsKUSo8JFuXC2aa6yxBuBvXB0jKvRAnzVrlius0vYqzbHscN68eQCcfPLJLnSvRUhhzZ133hnA2bBaJc6YMYMrrrgi0jEvXbrUOdKaJ9nxlltuCXhbWrFihZtDPcQvvPBCwBfb6LgqJnn22WfZaqutIhlz6tgVWlaoWXOmYid9ZllZGXvttRfgHVY9DM4++2zAP+iVQunfv7+7JlEWOcXjcefAasuGekQHCzf/+OMPlwLQ/alQqJo8yO71da211nJOxPHHHw/4+7SmaL2So3Heeee5NUpOqOxE40pN6dx+++2AF3AKz6r5jv728ccfB5Jrem3C5Ba2NQzDMIyQhFKeRUVFzJgxw4VYlHidN2+e87KkvLTRPdjOKR6Pu9CEvDAlciWjd9llF8DL9nQo0NzcXEaOHAl4z6hLly6AV77y0H755RdXzCS1ptCR/kZh2wMOOABIqqO6lJqXlZW5IiuFbQcNGuSKiObOnQt4BSM1ofDUggUL3LE09wpbyGO//PLLAZxXXNOw8soINmSWEgK//eS///0vEE55pjagAK+GmjZt6n4Wla0kEgnngasg5Z577gF8hEJNGg4++GCn2IIb2xU1SMe2g1Tkrf/www/OFhSNkFLXfMlWf/31V5daUMpEhU7/+9//AN8yU8VfHTt2dCGuuioiFYJtvPHGbr7UFOGYY44BfLhQodFPPvnEfa62qqgJiexcIVAVwLRr186FfaMiFos5tSx71DhkNzq/eDzOcccdB/gUiSJWH3zwAeDvX7WQ+89//uOiSlFuBykpKXHREKlfFUhKkUnxXXLJJYwdO9adAyRtPZVguqisrMydt+ZByrymaP1Q+iwvL89tmZHiDd5PGt+MGTPcdZftnn/++QCu3aG25miuO3bsWKs5NuVpGIZhGCEJpTyzs7Np27aty7tJuWy44Yau7Fk5Cnll8hL1NScnx6mm5/RRFwIAACAASURBVJ9/HvDeudTqaaedBvgcU21eobQyYrGYy6MIedf6/tVXXw0kPTGNQd6gCg+Ue9TWFSmfKLZ8BLdqFBQUuK0dQh6TPDHlUEpLS11OWtdLXqKaJqhIRGONSh0FE/K77babK6DR1gPltFK9c6E5DLYV1DilqlXo1bVrV5fXqKvy1HGefPJJp8KWLl0K4LxwFY0pcnHAAQdUaFCtr5lCc5R6DRW5kMpROzv97nXXXecUmSIYylMpwqHro3tx2223jazBtv6+Q4cO7nNPPfVUwEd4VEuhfH1ZWZlTSCqMevfddwGv/HSeyvlfccUV7ppF1QQkKyvL2Z/mSFGU4EsPSkpKXO5YKkxFO1Kiytcqqjd48OC0tMArKipyhVW//vor4AsJlU/U95cuXepewqDol1pmVrUmx+Nx13qwtnOu81UB59577+0iE8HPDbYYveOOO5w6Vd3BPvvsA/hGJVKmWou6du1qytMwDMMwMkEo5RmPx2nUqJHLpcijjcfjzhuUlx4kdduJ4uNqTaWYu3KM6cx1itLSUnceyqconi8vXJ5rfn6+q3xVlag8sGA5djrGnKpm9TnBbTz6f2q1rTazazuNGhRIuSn/GLWyl8esfPd+++3HO++8A/g8g5SMFJuufTwed1WG2sKkqkZVTypyoarv3r17u+NFOXbZgSrHlTNRjljjLC4urtLuM4XsonPnzq51pKIjOg/lY1Wd2rNnz3INE8C3SVQFZpBEIhH5y6+Li4tdrYDuOeWXpcwUxTj33HNdREUNKI499ljAR4WkVtVE4fDDD49821tubq6r+RDBdpKpakbRNTUpV42IjqEokNRzSUlJ2tYSXWtFTm644QYAd4/KTgYPHsymm24K+LqQleW5Y7GYi8ZVpRZXhj5DudntttuuShWu9VfX/M0333Qvh9Dnajucqmu1xU1Ku1GjRqY8DcMwDCMT1KpJgp7oii1DuMq7YB5UXqH2UEpxyHNJB0VFRS6/Iq9KykyKSfu12rdv7zxyKSXNQTrysTUh6IEFW9aBV/BqAycFqtxuulH+bffdd3fKQvkVVaoqhyuVfNddd7nqVilM7X1TVbY8e+29veiii9x1qWseThXHO+64I1tvvTXgqxCDzd7TXUEbBtnhJpts4qoJ9VJxqRntQVUuNHX8ldlPpkgkEm5uL774YsCrfeU1VXU7dOhQF3GQ0tNeVdmHKv6V+2zbtm2FFo+1RRWkX3zxhVPFwT2p1b3YQuOQDWvvYbC+IZ1oXIqWHHbYYYC3D92LeXl5ztbDVOJLVQfbbNYU/b4awbRo0aLK+zrYkKVRo0au2lotHdVPQK0GVcuiKFhtIymmPA3DMAwjJLVSnnV5/VMikXAqQR698gFSgPI600lZWZnLDSlnopyWcgLKo8ViMecR1ie1sTLkjSmHoX218izT/ToheZAtWrRwr2NTRbX2F0ppKC+3YsUKN//KKeo6SL2qQlR55/z8/Mg99lgsVkHNRp3ri5LU1oXqdKOvIliZXZ/Q2BTNUkWo8rap1diKSMmmpDB1XsqP6m+Ki4vrrDh1LN1TDz/8sFM4Ukhat2piJ7peqypyBf7+1DqojkO6FrWtGI/qnLSDoaysrMpnjT5Lcz9q1ChXLawIou5j7U/WelLX+9mUp2EYhmGEJLKXYdeU4uJit+dpu+22A/z+KO1H7NixI5B+T18elrxS5V1EffTQwxB8dZxyhLXNRdSWkpISd42VX1GXI3mJynM3atTI5eRUgShPUU3Lg82g0+G9JxKJevNi7TAkEokGabey0WA9RLDnaCKRqBAxkXIKHiN4f9cF5SiVb33iiSfc56obUmW55IaA5ikTL7YOQ03GE9wTvuWWW5brKVzZ8aJ6rmT84ZlaKq33TKqlnB6m+nmwoCidY1qdqU8hIqEN1HogagsQVH29V3WRllE/qa5AJypSUxCQ3MahMKfaBJpdrjqibE5TUyxsaxiGYRghybjyTC2+UVN1vetT4blguNFY/TAv3WhIKOSnRgxq/QbpbZBi1F9MeRqGYRhGSDKuPKFiYl/enHluhmHUZ+pD/YBRPzDlaRiGYRghiYVRe7FYbB7wW/qGUys6JRKJNlX90MYcGdWOGRrmuBvimKFhjtvGHBlmH5mjyjGHengahmEYhmFhW8MwDMMIjT08DcMwDCMk9vA0DMMwjJDYw9MwDMMwQmIPT8MwDMMIiT08DcMwDCMkoToM5eXlJQoKCtI1lloxadKk+dXtHcrPz693Y544ceJqN2ZomOPOy8tL6OXg9YXVea7r25hXx/UDGua4G9qYQz08CwoK+OCDD6IZVUS0bNmy2k21BQUFjBs3LlPDqRFrrLHGSsf80UcfZWo4NaJZs2Yr3bxcUFDA+PHjMzGcGtO0adNqx92pU6d6Z9MtWrSo0Vx/+OGHmRhOjWnevPlK7Xrs2LGZGk6NaN269UrH3NDmGRrmuBvaWr1KetsahmGkC724Wg1gMvXSd+PfheU8DcMwDCMk9Up5xuPJZ3km3gy/uhOLxZwHLs/bPHAjSPCduQ35ntO5LFiwAIAmTZoAsMYaa7h3bq6K8WRlZZGbm1vue3ori76uynnXmBryta8OnZ+eL3o3a10x5WkYhmEYIakXylOewYoVKwDIzk4Oq3HjxkDSO1tdvaKokdpcsWIFc+bMASAvLw9IeuBgCrS2yE5ln7LJ6lRNTk4O4L1e/W5U3m9t0Hnk5ORUsAWNqyHdb5rjqVOnAnD22WcD0K5dOwAuuOAC1l9/fQAKCwvTPh5da/Hjjz/y5ZdfArB8+XIANtlkEwA222yzcn+TyXsz+FnBXHF9QmMLjlH3U3Vj1nNl0aJFALRv336lf1MTVunDU4vQTz/9BMBZZ50F+It68MEHA3DggQe6G8QW/srRXP78888AjBw50lWRbrzxxgBcf/31gDee+jiXwTBidWTqJg86d6oIXHPNNQHYfPPNKyyYegg9++yzAMyaNQuAgQMHAsnKwkyHEmUj//zzDwAPPvggX3/9NQAdO3YE4IQTTgCgWbNmQP20kaoIhm11nX744QfuueceAPcQjdJ5SQ3Pgn+I33TTTQBMmjSJP/74A/Dz2bZtWwD23ntvAM4991zAO7rpfNm21lJd+/vuuw/wTodsYVU6eKlkZ2fz1VdfAfDZZ58B3j4HDBgAQMuWLYHyY9b1+PPPPwE477zzADj55JMB2H333YHaz7WFbQ3DMAwjJJErT3lh+lqd56qf3XDDDUAyvAE+lHHxxRcDSWl+xBFHlDtufQwtZBKdv0Lb2hcqr2rFihX07NkTgLfffhvw3u7NN98M1A9VEfTaE4nESq9tMPGfbluQp/7+++8DcPzxxwNw0EEHAUnlGbRL/Y3U6rXXXgvAiy++CMA999xD9+7dgfSqDMAVq/z6668AXHjhhQC89957bnyNGjUCoF+/fkDynKB+2MjK0PxpPrVWKE1x++23c8sttwA4BRqFqtI11/w+8sgjgF/PlDZZf/31GTVqFADrrrsuAN988w3g7WL69OkA3HnnnUBSgaZj7mOxmJsvjfeBBx4AfEh75MiRQFLxrcp1VmvC/Pnz3TxpLdO4JkyYAMBVV10FQPPmzSsUSKrxQrdu3QA4/fTTAXj44YcB6N27d63swZSnYRiGYYQkMuUpL0wJcXkxikWn5rLkUfz+++8AfPzxx0AysQ8+73LUUUcBcO+997rYduvWrYH0xOODJc01yb/JA8p0fkDerjzYM888E/CKZ9SoUfTp0weAww47DIAvvvgC8NdG56lcWFFRkfPW9L2oCX6m8n7qhvLaa6+xePFioOL8a2wbbbQR4FV2VlZW2rz0VJRDlv0eeeSRQPJa6PODCvSQQw4BfC76uuuuA+Dpp592kZV0RVM0x8q3Ka8m771Jkyb06tULgClTpgAwceJEwCvPykjnlrJgUVYwupCdne3mOnjP6fuDBw8GfKTl999/d7nnqMYai8XcGKVgVFMghd+7d28gqSZls7L3rbbaCoClS5cCcOWVVwLw3HPPAXDqqaemrbhJylNrh87jl19+AWDZsmVAMqcfdr5isVid51g2oOt7//33u6hPmzbJTnnKyz7zzDOAz2VrTQB/rZs3bw7AnnvuWe5vdB/06dPHlKdhGIZhZIJI5EU8Hnde0uGHHw7AWmutBcCtt94K+NxcWVmZU0fvvvsu4PMtu+22G5BUQIDzit9++22XmwlTjVkdiUTCjUPHVBWiKiOljCv7THm5+fn5APTo0aPc75aUlEQ21lTk9UvhK3+5cOFCAB5//HEAtt12WzdGqXVVqml+VdmnqsSbb77ZjVnHqYuiTlXyUmtz584FfKXfd999B8Btt90GwOzZs6v8TJ1P06ZNy53H6aefnpYyex1z3rx5AHz66acA7LzzzoDfblBSUuLK4HVdtE1CNnbssccCfl5fe+019z0ppKiqbzVuKXipmrfeegvw1/3oo4+mb9++ABx33HGArzsIkpqb1n2ic4sC2bWOPXr0aAAXPdF68swzz9C1a1fAK7ugOtU9mapeoxprapTg3nvvBWD48OGAV2wbbLAB4Ne1+fPnuzHqGusa6RwUoXvzzTeBZFRDfx91VEXzFIzwSM1pvajOHoMRJJ1PYWGh+15tc/kaj1T5hAkT3L2u72233XaAv/bKFe+6665O5etv9FU5ce020Hq4bNkyZx9h1g9TnoZhGIYRkjopz1SV9eSTTwJexfzvf/8DfIusVDUhz0T5lRYtWgDeW5en8NJLLwGw3nrrubh1VF5YTk6O218qb085ACkM/TwWi1WoCpVXJm/t6KOPBuDQQw9156JzjlKBau4effRRAF5//XUAV00oT72wsNCNVeNQpZ+iAC+88AIAp512GpDcD6W9T3VpZRXcF7l8+XKnKK644grA53aC5yVvuzpkH9qftvPOO7sckn5WV1Kv+WuvvQZ4+zj//PMBP0cLFixw+c8OHToAPuKi81KuRtGUV199lb///hvwdh/VuIXyfC+//DLgFZmqbY888kh3boq2SDUFc4/6/0cffeSqM/fbbz8A9t9//zqPW5+j8Zx00klAci8qeBVz1llnseOOOwK+WjTYtELX5bfffnNjDp5XbdE99eyzz7oKT9m51iitfVtuuaX7eVCFaR1r1aoV4PcMK4K0cOFC1llnnXK/GxWaH63NQbWVumNCv6uvqrWYP38+gNt/+f333wMwY8YMN9fHHHMM4KMxNUWfr3t58eLFbt6Vz1bFu2xPEc/Ro0e7iJDQ/Ok+U370k08+ceew/fbbl/vMmmDK0zAMwzBCUiflKZXw3nvvcc011wC4r6oyrM5rkjehakDFs6U4FZMeOXKk88zqqizkOX3//feuQlWVXBqPcipSM4lEwnnmytnJa5s9ezbg8x7a2zV8+PAKHnFdycrKchVxt99+O+C7MMkj0/zk5uZWUNLy5hUluPTSS93vQnI/lFRJXcaseZSiHzlypFOw3377bbnf1RwFO/RA1U3L9TfKM86YMcMp7qiIxWJOGUppbbrppoBXFOL22293nre6ZCkvG8wbKbdV2flGNW7ZqPY06h7cZ599AJ/fLCsrc5XuIri/Uz9PjSypg45yY9rvWpcxS53oc9RBZu211wa8kl+2bJmLYsjWla+S3QlFN6ZPn+4iHrW1a12vJUuWAPD888+7nKE+d9dddwV8dEHfb9KkSYXPlV3oRezKw0nJTZ482e1PjLITVTweZ8aMGYCvrtV91rlzZ8Cv6yUlJS76pkp9rZVS9aosVhcfqFgpLXurzVh1PKl6rWGKokmd77vvvkByrdF56Bkk29K+X9mU1vTvv//e5f7DUKuHp07qr7/+ApKLx3rrrQfAkCFDgOrL2DWpekjp4ilEow2xuikHDRpUZwOSIf/www8AnHLKKW5h0GJ4wAEHlPuqwoqsrCxeeeUVwC+OKg4I3rC6+XfeeWe3vUZhnbpSWlrKiBEjAB96lQMQfFDPnDnTtaNS4ZO2Wrz33nuAb0+ltlyFhYWuQUVd5lvXU9fx66+/djajEL1Cbyq0UvOA1JtQRSKyFz0shQpt2rRpE3loKzc314WFJ0+eDPjN7wr/3H///QDcfffdrogoWPQmglu52rdv765hlEVOOTk5LkyrhU0PfYXnNZaff/7ZFeZoLJ9//jngC5sU+pUjEYvF3CKkEHVd5z47O9ttdtfnKyQs+9CCB36rkr6nudZiqK0jN954I5BcvLfeeus6jVXXSA+WzTbbzK0fcvp32mknwDtIWiNqcjyd0zvvvAP4dSpqsrKy3BYNOSFBZ1QPyAceeMD9rtaw4PYZOS6yCfDPBRUFht32prnR2tq0aVMX3tZDU9dcv3PiiScCyeJShc31QAy2PNR1uuuuu4Bk+lBOUZjCIQvbGoZhGEZIaqU89bSfOXMmkEzyP/TQQ4BPmgc9lNRtC3qq77HHHoD3AFSIIVUybNgwIOkV17UJgZSP1NC4ceNcU2Y1cJbcl3eaWoDQv39/APdVHnmwoELe2+zZsyMLzSms+umnn7rtBkOHDgW8epdXJS94+PDhrvGAxvHGG28AcMYZZ5T7Kq+urKwskmYPmjd506lbBRQWVJhbikfJ+99//939rjz34PXQV4WDdthhh8g2lGuuCgsLXUGVFI7UpTzzSy65BEiG8lSEoGsVbJqgUKrC1uuvv767V6LeXqPxaf4UTZDXLhUxYsQINy6N+7LLLgMqKmeFoePxuAv/qkijtpGV1MKyxx57DPAKRgVYmiPZNfg51DYtRUl03rJzFZWcffbZFYrnwhJsu3jcccc5VabQppR4baI2mXqvanZ2tlsXdM/oHlTUTFGHsrKyCg08gioy2AovFou5SIfSXnWNGpaWllYoXBLB1oz9+/d3dqGCMjUH0bVX5EhRsFmzZjkb1n1gytMwDMMw0kCdCoZSlZme4orhV+UhLFq0iDFjxgB+q4EKhqREFbNWziuKxtkaa2oDBrVHU75WOYAgpaWlzvO++uqrAe+BaauIPBeVSffq1Suyht/ydidOnOiKFPbaa69y56WYvQq2nnrqKfcznd+pp54K+HZ98sY1J1FtqZGHpwbTc+bMcd6tVK7yQip5D7Z8A58fTN0SBb6sX0VSUeQ7gy8yuO+++1zORmpZRRPKz6p95Ntvv+1Uj/LJKijT+SpfqkKL8847zxXcRN0YXnOoc+nSpQvgr/cdd9wBJBVacOuVvmpsG264IeBz6507d3Y5JN0TtVVz8vI/+eQTtyYoGqSohQp9FHHp3Lmzy4+qoFD3h9Yg/Y2KS5o0aRJZ0Y3sZNmyZe666RVoWse0NlQXDQm2oFNj+Ew04g+qxareSxuLxSq069S11/0sxaciqd69e7v1RlujwkYmNB4VjW2wwQaukEoqX/ah39VnnHHGGe7+VE5a10frhqJ1ujf/+usvdy3DrIGmPA3DMAwjJLVSnvJG5Ol17drVqUUpoKBXOmnSJCDZkk9vVZeHIi9XSkK5x+qq1cIir0ped3FxsRt/VYqzMqSGlSc98MADAV/pJ+XZo0ePyBVFUVGR857klanhuJSNcs/Z2dnssssugPfEt9hiC8ArnXQ0cQDvDUpdaszgbSeocLRJ+YMPPnBqKNhsQd6mqoPVeCAKb12fqTL+m2++2X2utvwoUqIXGKiaeo899nD2r5Z7ytUpv6JcuBrDDx482M1BlPmtRCLh8oZSdrrfFJVQRAD83Cmvq3oDlflLUeh+TiQSVTZmD4sU43fffedaIMpmpBqVv1Tl+ODBg3nqqacAfw8EW2Tqa/DlA1GQ2txA65SUsKpMg69lrOz6pjbYAN8qT3OiyEXUFBUVuYiJcuDBpvmpURhdDzU8UGRAtqUtNoo4ptpHUNnWlODrFrfZZhunJqtSsamNEGQr2nanHK7qRFK35kFyzdH9qTWlJpjyNAzDMIyQ1El5yqs+++yzueiiiwD/OrFg1ZLUTteuXV2lpfZTypMPtudLB/KgU8cWBnmx8opUfStPMpg7igIdq0ePHu5zBg0aBHhPTBuetWf1lFNOcSpC+yHTOa+VURNlovPR/uCioiKXP5Qnr31Zagih/Vs6nyiUm2xakYXDDjvMVYFr76aaSkhxqAJ06623dmpHylXnrq/yaLWpu7i4OC35rZKSEteyTC9eUJMMqRpVhcbjcddOUnt+lQ+Sfeu+TccLu3XMTTbZxOXOtHdWyksVs1INjRo1clX5WmOE7pPg3EeJrlmTJk1cDYHycWoUrwjJNttsAyQVclDV6Vpon62OoaYJG220UVoqbktKSlxDAd1XivhVpjwVQVHLveB+cs1xOtYWHbt79+4MHDjQ/Vtjq4yysjL3XBk/fjzg9/tKJStaqEic6hTCYsrTMAzDMEJSK+UZrOYbMmSIe7WOKuDkVSqnpb0/7dq1K7dnDHwuJsrq2pWNvbYE8xiZUHOq2ttpp51crlUtDOUZnnLKKYD3Ilu2bFllFV19QtdaHvewYcNcHkhzK7uQtx6l4hSyZamZww8/3CkHKV3ZbbCKsqioyCklKdCqjq/zTdc+vuLiYleJrVeRKWerHFDq6wF1TsGq20zadZ8+fVxXIFU49+zZE6jYqD71VX9Rde6qDYlEwu1jHDVqFOD3/UrZKD946qmnujnX2FUDoo5hmnflFvv27Zu2a6AaD+Upt9122yp/Nxg5zORaos9cf/31XRP+lb16sLS01K2J+hu1UFV3OOU39QL47OzsWu3JN+VpGIZhGCGJZJ9naWmp67AS9LyDKjW1i42+RtUjc3UnkUiw5557An5PrNRYUNmkU72ng9QOJdpLJjKpoGWTXbp0oVu3buU+t7o51fgznVeuDI1F+Uz1iZU6Tt1TG1XlbF0oLS1164aq1TWeYOUmpE+1h0XXWpXiUs/KfapS+LDDDqvQmUfVxYrMHXHEEYDP62fC1jWnUXXnShexWKxCD/HqCHYS0gsSVGujCIGu37777uvWnDDPoDo9PFOpS5LeHpo1J3hTrcpFLx0kEol6sTiWlpY22LkNFn5o60plD6L6QjqLfNJN8H25aiuqZuVvvPGGa9YvB0YpAbU61N8qlNoQ56G+oTnUNiy981hpGL2EYr/99nPb6cLMu4VtDcMwDCMkkSlPwzDqF9W9FtCIHkWFpPg7duwIJLfvaQtfkGBayxRn9GhOpeqVzhC1fSGGKU/DMAzDCIkpT8MwjAhpCFvE/o1EnfM35WkYhmEYIYmFyYfEYrF5wG/pG06t6JRIJKrs5mtjjoxqxwwNc9wNcczQMMdtY44Ms4/MUeWYQz08DcMwDMOwsK1hGIZhhMYenoZhGIYREnt4GoZhGEZI7OFpGIZhGCGxh6dhGIZhhCRUk4T8/PxEQUFBusZSKyZOnDi/uvLnvLy8hN4VWV9Y2Zgb4jxDcq7Vkqy+MHny5NV2rs2u687quH5Aw5zrhjbmUA/PgoICxo8fH82oIqJp06bV7gvq1KkTH3zwQaaGUyNatGhR7ZgLCgr46KOPMjWcGtGsWbOV7r/q2LEj7777biaGU2Py8/NXy7k2u46Glc11Q5xnaJhz3dCeL5G359N761Lf9dnQ0PsO1eC5IZ6DYRjG6orWaH1dFa0QLedpGIZhGCGJRHnGYjGWLFkCwNChQwH/RvS9994bqN/qTSpZr6zRufz9998AtG/f3o3fOjJlHkUzcnNzAf8GeGu8bVSGIkZZWVlAcu2pr/et1hzZ+IoVK4D6vV6Cn2N9zdTr7zRfjz76KIBLE40aNQrw85gJTHkahmEYRkgiU55SA2+++SYAU6ZMAWDzzTcHkuoN6qdHJW/l22+/BWDkyJEATJo0CYARI0aw9dZbAz7GbqQHebKp//79998B+OyzzwDYbLPNAOjSpQsQ3SuGjIqkXg+on5EXjTEnJwfw9vDbb8laj7y8PJo0aQKs+vEH6yhef/11AP744w8A9thjDwDatWuXsbEGVWQqQUUZXP+07mvus7Oz0xoR0uf/9ddfAHz++eeAn8+cnJyMzVskD89EIkGzZs0A2HbbbQF47733APj6668BWHvttVd6nGAIIN3ooamb7IwzzgBgwoQJgDeIoUOH8txzzwEVF2yFhnRRUwulVvWN2pDQ/JWVlbl50/xfcsklALzxxhsAbLHFFgDceOONAGyyySYWwo2I1OsAsHjxYsDfmy1atHC/u6rsO/iwXLZsGQBPPPEE4O1k2rRpAFxwwQUcdthhAPzzzz8ZHWuQYIpo+vTpAJx33nkAXHzxxQBcdtllFBYWpnUswWtd2ecpVaJ1TvZw7733AjB69GgAOnfuDMCZZ55Jz549AdKS6tKxZAMKc0+dOhVIrg1h14KsrCw3B2HGajLKMAzDMEISmfKUF9i2bVvAy/mg55qKPJM77rgDgAMPPBCAddZZp9zP04U8FCWbFQIYPHgw4FX05Zdf7jyss846C/Dn8+uvvwI+cb3pppsCsNFGG1VQo5lAajo7O9t5i0Lj0LWpD0VQGuPChQsBuO2225gzZw4ARx11FAA77bQT4FXP008/DSTD6QAPP/xwxqMWDQnNseamsjC3bHX58uUA3HzzzQA8/vjjgFdK++67L+eeey4AzZs3r/J46SJ1HZHauO222wB46aWXAGjcuDHgQ6ELFy5c5emWqq7BQQcdBMDYsWMB+Pjjj8v9fjoIXuvrr78egDFjxpT7eSKR4JBDDgHglFNOAbxdvPDCCwC0atUKgNdeew1IzvlTTz0FQOvWrYFo1vGg0lRKTevGn3/+CcBWW21VY+WpOZ46daqz8wEDBgC4NF11mPI0DMMwjJBEVtcr5SnlFcwJVqYI9L37778f8Elg5bjSqdyysrKc96JcSZ8+fYBkjgRg3XXXBeDVV1/lww8/BLwaUk73zjvvBLxqVSuvSy+9lIEDB6Zt/MFyfM33999/D8AXX3zhCm30+S1btgSgb9++QFIdQ8XcRyaQQlYO6vbbm3VoMQAAIABJREFUbwfgnnvucePo378/kMyjAPzwww8AfPPNNwB8+eWX7mvv3r0Br6r/zWhuNReKjkg9qngPvB3JW3/kkUcAHw2SbcjDf+WVVzjppJOA8vnPdJO6BeHFF18E4KqrrgJgwYIFAFx77bUAjBs3DvBqbqONNlqlOfF4PO4KKNdYYw0g2Y0r9atyhlJW6bwXNZc//fQTAM8++ywAM2fOdOOFpE2o489///tfwEcHBw0aBPgakOuuuw5IKlPZSn5+PhCN8gza4axZswBcIZhqamryWTqWcrzXXXedq2np1asX4KOO1R6nxqM3DMMwDAOIUHnqab7lllsCyVJr8JVw1f2NvLHHHnsMgP333x/w21yiVBOp1W7KU0r9KN69/vrrA17V9evXj7vuuguA448/HvCVfHvuuSfg82+pX5WrW3PNNYFoPDCNSd6jqvU0PnnlUvEAxcXF5f5GeYr99tsPgOHDhwPpLfMOKmU1otB8PfDAA0Byjrp27QrAxhtvDPhmFfIu5RXefffdQDJPJLuLKveZmltb2bFS82k6P1UpCikJXYt0VWNnZWU5RaFclpSYKjqPPPJINwaNV5vOdT10/hr3vvvuCySrQNu0aeP+Pt3IZn/55RcAHnroIR5++GEgmd8CuPXWW4Fkb1TwebkNN9wQSOavVkVEQrnX2bNnc9xxxwHwn//8B/DNZKR+tJ7ss88+QPqUZywWq1CvoXyh5mvXXXcFktGHvLw8wK/nuvZC9qO185FHHknL2HWPzZ07t9zYlXdfb731gJrZpGxKa+WYMWNcRFHRrprYiylPwzAMwwhJZMpT3oy8GFVMLl26tNzPY7GY87jlmfXr1w/wzQm0N1TKM/Vv6oo8pZkzZ/L2228DPk+pcchz0pi7dOnC/PnzAb9h/4YbbgD8pmZ5Rspznnrqqe48lGOsLRpHdna2U2HKU6hS+LvvvgOgW7duABx33HEuz6K8hdSQjiG1p3zL0KFD07a3TPOjPKUUjnLHIhaLuby5PGF5gcrZScnrOi1cuDAybzd1E7vmS/n8oA3qd5ctW+bmTfb/xRdflBu7PHjlVDp16uTGHMXYNb/Lli1zClP7HRUdUatMfV5OTo6L9ij6IJRLUg5Ox+jWrVtG9krqWqvW4OSTTwaSiuP0008HfG2Ccq8XXnghAD///DOAqwpu1KhRRpSn7EHXQjYwfPhwd48pVyjb0n2saMHuu+8OpK/1ZKoNy641XtnobrvtBsCDDz5Yoeo3OI+6TsE1M93oPJQz1jiqq63R+WoHiCIz/fv3dzlbRUFrlDut9egNwzAM419KZMpTT3d54Pq/VF1q5x15J/IAFL+Wt/Xpp58CPv7frFmzCq86q60Sldp9/fXXXS4otSUWeE9MeYg77rjD5apUdSYPUecrT7J79+5AsrL1mWeeAWqvPIOvRhs7dqxT5++//365zz3iiCMAOOaYY4Ckcjj88MMB7xVedNFFgN8Pp3mePHlyuc+LmuzsbN566y0gWYUM3tNWDkWVeT/++GOF+Qq2NJOi1njbtGlT54ph/b0iJcOGDXP74IJVg0Hb+/HHH10VoCIUUj+yG+VmFBnYcccdnVKScqqLAtX4582b5yoRVS2uamXZt+bznXfecRWrUppSa7fccgvgWyFKjUiJRo3GJHtWPYLGrrkZMWKE6xakCITeW6mqfdUaKA+na5AugopT3XekZlq1asXzzz8P+CiP1j7tidQ5Kd+fCaUse9bcKioiWwZfwxJUYsHaAnVpW7BgQUb21OpzN9hgA8Cv65Vda6lSVeuff/75gLe1YcOGuXswzLxH9vDUQ0QLs7ZFaAuHet4uWbLEyWf1ktVDSi3+9NDRS2h79erlLqzK5HWzhyU11KYLsMsuuwC+kGbRokVAsjhC5yCD0Pmo4KW6cdTlDfSxWMwZgm7CRx99lHnz5gG+aEaFB0p0K+xwwQUXuCKLnXfeGfDNH9QjVmM/+uijgegXGYV8FixY4BZjjUk3pTZfq/DplltuqdDeS0auRVLXQA+i/v3719mpCm4cnzRpkvuc4A2lh2lqiEcL+VprrQX4BVxzrDTGO++8AyRTFHJ0ZHdRhG/feustN5dynnT9dX0/+eQTIFlApPGp+EoNSoYNGwb4xVznmq6CMjnH2mx/2mmnAb5ITJvYO3To4H5XxSNBB0At7rQGpetBFLSZm266CfDhchU+Nm7c2M297j1tcVOY/+qrrwbS3+QjFos5kaJUj8amohs5p8uWLXONDqpCNiv7ztR2t5oUBur6aD1Xqkj3tWyta9eutbIRC9sahmEYRkgiUZ5ZWVnOo1JTdXk3at4tjyRV0uvfUijBDf8qzvnxxx+dl6BNuWprFRaNa7311nObxYOFIfLMpZYPOuggp/hUfCNvRh65kNe/YMECd7ywxONxGjdu7DaqS7V16NDBqWGVvOsc5ImpSGnMmDHue5orFQTI09T8S/FH7fVKIUybNs0pTm0/UbGSthdIXScSCac4FYr56quvAB92VlhSirldu3Z19nhlF1KOjz32mIt86NrrMxQqSm0SoLaUCkNL9cgGFNZSqLxLly7u7+sy78HN46NHj3bzp+ut66DzkdqfOXOm88YVyZD9pqZZ6jrGqtC4cnJy3PqhMK3Cm1Jkuu9LS0vd76poT2uOFKiiGukO1+raas6kJtXkRQ0FLrjgAvd+Yyk0qbzLL78c8FGqdI859TNUjKVwviJwWvcaNWpU5X0VbJf38ssvu++nUz0HI0yVFSjpewrX6hmk7VhXXnklkHyhBNR+zk15GoZhGEZIIlGeubm5bsuEYvjKAXXo0AGAHj16uN+V+pAHr0SuyuX1NypJlwcNPqld21JuedJrr722G6MaTKvIQ+pO5fnDhw93iX0pT+U5pJbVDEKFMStWrHDNFmpDLBZzW0p0zhdeeKEbU3DTvfI9as/322+/OeUmZSlPWWNWPknl3lF7jPIAZ8+e7ZS6vD3l1vQ7qS8DUKNvjUtN+WUnynUqh9uyZcvI8lqa1/bt27sirKryqaleuf4t+9J10Vd5wVLL++23n1O5ddmWEMzrfP755y4nu9deewHJlofg29fJVm+++WbX+FvjDDYulzqMsoWj7E/30r333utaZcrmd9xxR8A3MJGy+eyzz9y9qEYg55xzDsBKr1fU6LrpnZy6nw444ADARzEuueQS16Re86htWIpUZEJxQnLuVaCpNpdS+YqEpNpCVVs2ZBe6Lrp+AwYMcEo2HflPRQm1tgWLTbOyslwxllS9IgJqDnLCCScAdbcPU56GYRiGEZJIlGdxcbFTAfI6VOKuFlrKWWRlZVXYtKo8kHIF22yzDeBb4aXmSeUJ1VV5tm/f3r38+sknnwTg0EMPBbx3o7Zfa6+9tqsAVY5T3oxagSmH98orrwDJBvlqVh7WwykrK2P58uXu9WfyrBOJRAWFIDRHapK9dOlSmjZtCvicnfJuUnDaNJ+uV0vpePPmzavQIjDo0W6//fZAckuEXo0khaS/kRpRXkyN/NNRTVlSUuJsLJhXqY3HKq9eDQzKysoime/gNp7CwkKXb1WOWDlCKSPZ6m677ebmLvgiB9m5bEaRlqZNm9Z53LJV5Z6+/PJL93kaj/KZ2siemnvV66J0f6qdXLBmIp2kVsNLQWvNU/W07KRLly4uWiKCkaN0k7rtTU3QtVbo3lOEKjXSp3oDbaXRdVKzkyuuuALwKvuss85yEb0o70vdi8oNK4KlSJ/yzhtvvLFbz2VDyj3r+aLzrGsjClOehmEYhhGSyJSn9jSpgbTUW2ojbCjvFcozk6emXKcqSPXzyryz2raB0ue3aNGCY489FvD7xeTlarO1KigLCwudipSXq9eYSdWpQld5uhtuuKHOr+TR39Xk7/U7Uvj5+fmuAlN7+OSRKY+kaIE89qgafQebiv/111/u38r1BF+bpXkbMWKEy2lJxQ8ZMgTw1YCq0M2U1x5F7qw6W64LmlepzV69erl9elKN2hutqmu1P0xtxajjSEGoKcJDDz0E+PzR+eef7+y6tgpPdqYK619//dV9rvJV2oOophVaGzp16uRydGpIUtnakm5isZi799WGT5EiRXxS5zcTTfQrI/jKuYceeshV8UshqmWgFJlqUtq0aeNe66aKZlULq0pbVfSqiu7Tp09a7kvdP1o39LxRvllz37FjR9fyU69cVA2L6ip0XeraStCUp2EYhmGEJBLlmRr/D+7/qY6g8lR14A477ACk5yXNGl9RUZHLrenVNFKV6g4jb62srMzF+qVWVd2o6lbl384++2wg2dQ+U8oIvDelvODpp5/uurKoG5IUvVSzPMx0dWDR9V2xYoW7llINQTTX+fn5rgm45jrYxSmT81rfkaKRGnz00UddTlsqXz9TNKiy6536qj7wnau0p1aV6CUlJXX22HU/68UPm2++ebkXR4CvdNe4UveCy1ZW5Quus7OzXe5Qaij4Wrz6QOqLMCCp9nU/qW5D7UkVkZKi33///d3vqNWhfkfXUPvNda+m61V7Qp+reg110dJr6saNG+dyuNq9oT21svuoro8pT8MwDMMISWS9bUUYr0NehGLt11xzDeA95HR4lvISf/rpJ1eNqD2oitsHmwTHYjH3b1UPK4+oijXF05XvyLQ60rxL4Q0dOtR5lMobKVeoXG66PffUZt8al3KbVUUTUnND6bSD1Q1d//bt2ztbDL7yrCYRBs21etpq/7Zyke3bt48sf1eTe0Q2FNw3u6rJzs52L5ZQJa0iZul6rV9t0LXSftK7777brVFay2QfsiHdd5deeqlbK9RvXC8bUG2LXpAhNZvuezXYWUhrtvo3r1ixwp1XumsjIn941gZNhC5qOmW/Lm6HDh144YUXAF+arYd4ZfI+mHhXsl2Nk+u6hSYqUo1LTkFwO0OmDFwPzO22286F/xQqrskCnO5N7qsjUW2BkY3IvhX6zbR911cbKC0tdfeXttYptZOuN8/UhuC2wNSXKGidq6r5R5MmTVyjGm1V0UNSqTY9mFaVXUgM6T3KqUIn3Y6WhW0NwzAMIyT1QnmKTHqZjRo1csUrwfBWTRLKwb+pb6Q2VFhVyAPcfvvt3Ts65aHWV0VhlKe+2/mqorCw0L22TdQnxRkktXivpqS+e1lbiap6b/OqojbnFRWmPA3DMAwjJPVKeWaaVZ2f/LcQVR7OMOoT/4b1Q8ru33CuYTHlaRiGYRghiYWJWcdisXnAb+kbTq3olEgk2lT1QxtzZFQ7ZmiY426IY4aGOW4bc2SYfWSOKscc6uFpGIZhGIaFbQ3DMAwjNPbwNAzDMIyQ2MPTMAzDMEJiD0/DMAzDCIk9PA3DMAwjJKGaJOTn5yfUqb6+MHHixPnVlT/n5eXVuzFPmjSp2jE3xHmGhjnuvLy8RKdOnTI5pJWyus61jTkaamIfDXXdq2/34ldffVXlmEM9PAsKCvjwww+jGVVENG/evNp9QQUFBbz//vsZGk3NWHPNNVc6Zr3uqL6wxhprrHT/VUFBAePHj8/EcGpM06ZNqx13p06d+OCDDzI1nBrRokWLGs31Rx99lInh1JhmzZqt1K4b4pgb2poHyXHXN7tu2bLlSu/Fjz/+OFPDqRGNGzeucsxpa88XbK5u+0kNwzAaNlrX9VWvHdT6HtW7XhsClvM0DMMwjJCkTXma0qx/yEvUm+L1f726rKioqEavYzPqH7qWsVisTt6/rr9eeqxj6RVUxr+L4Ivt9YKHf/75B4BFixYB0LRpUyD58vR/y9pvytMwDMMwQhKZ8pTHKs9k1qxZAOTn5wPJl09D0pMJxsuDf1tfXl+VGt+vL2OqDTqPv/76C8AVEsyZMweArbfeGoBNN920QZxnQ8qnV6Xkoxqzjr948WIgGUVo0yZZHBhGgepe/PvvvwF47LHHAOjevTsAffr0CX3MdBCPx905r+qxrIzUa1+fbbQ6ZBdSmrfeeisA3333HQCTJk0CoF27dgBcf/31zlZW92hF5GFbGUzz5s0ByMrKKvfzrKwsZ0hTpkwBYOnSpQD06NEDgJYtWwLJMCJkzvD0OdnZyWmRwcyZM4cOHToAFcMXDSHMqWtw0003AXD33XcDsGTJEgAOPPBAAB599NFVMLqao7nWW+N1LRo1alTvHvpBx1C2LNvKzs6O5B2Jurbnn38+AL///jvDhg0DYKuttgJq9xB9/fXXAfjmm28AePzxxwHo1avXKnloaVwzZsxwTuDGG28M1L8Hk65xqk3qOtX0msdisQqiYlWgFM8LL7wAwKhRowBvz40bNwbgjz/+AGD06NH07t077eOqqmApk3NlYVvDMAzDCElkylNPfnkEUo/ywuQhLFu2jLFjxwJw1VVXAfDLL78AcPDBBwNw/PHHA7Deeuu5Y6bTu9Sxc3JyAJ8El5f1+OOPM2TIEADOOeccwJ9XffN6U9H5fP755wA888wzAOy6664AfP/99wDMnTsXSCo6eZr16bxkU8uXLwdwyurrr78G4MYbb6RXr16AL37KNBqjPHGp4+eeew7wyq1bt24AnHDCCS4kGkWBzyeffAKUD2uGQR5769atATjmmGMAOPzwwwF45JFHgGSIX9chE2jdkNI599xz3Xw9/fTTQMXtE7JhUVhYmBF7VmpK69mdd94JJNXm6aefDuAiWCtToMXFxe6cmzVrBqwaBap17ttvvwV8KFYFZUKRxueff55jjz0W8OcaZaQiqOCVZtA1b9asmftZuq+5KU/DMAzDCEnacp5SPZ999hkA8+fPB+Ctt97ixRdfBLx3LuSdT5s2DfBKqWnTpmn1IuRdqYDm8ssvB2DMmDEAtGrVysX8DznkEAC6du0K1DyHkW4qK76S56pcpoq3zjrrLCCpfsBfqyZNmkR6Pqll7vIY5YXKi9a4U5V8VWPQ9wcNGgTA1KlTAbj33nu5+eabAe+ZZkJpaK5T85cPPvggAG+88QbgCytUQPfOO+8Ayfvi+eefB6Bt27ZA3WxJ57v11lu7nFNVSiV1roOqQMp9iy22AHze9McffwSSRWdS11EqIY1JaC70fUUZpkyZwu677w5QIUoye/ZsILnGpDJw4MC0qjeNUepf+edWrVoByWKa0047DYALLrgAwF2j4PzrWF999RUPPfQQAFdccQXg79+6onskWHhVWR2H1mite4qkaK1MLQSFZMQxeC2jQOuEooIPPPAAgOsep7keOHAgBxxwQKXHCEZkgucdeky1+ivDMAzD+BcTiYsQj8edFyjPQF6YvCblASrbqiKvRR7R9OnTAZ/j0gbcqNE45G2PHDkSgJdffhnwOVnwno7GXF/QvC9cuBDwFbTt27d3al8Vk5tuuingz1d/M3jwYCA5/1EqT13P5cuXu2hDv3793PjAV1pra0RhYSEnnnhiub+XfbRo0QKAvn37AjB58mQAbr75ZucJpyPPEiRov+PGjeOee+4B4LXXXgNgjz32AHyuUFGAK6+8EkgqUG0vUZl/XdB1Ky4udude1ZYeVUbm5OSQl5dX7nf0t1LDW265JeDzi1OmTHGqSedUV7Kzs13/WG19OOqoowCfQ1befs6cOey2226An3/VUCg6tGzZMgB3zHg87moWNAdRRCZ072nXgMYsO5VNtGrVyilO2bbuBzVC1/XT/Pfo0YMJEyYA/8feeQdGVXRt/LcpdCQUERFCVwEFFVQQQSy8IqjYey+IXcGKBRtYsKBYsINYsCPI+6Kg2AELxV4QRSwooCiokJDs98d+z8zN3QSy2ZJEz/PPwmb37rlzz8yc57TxbE9x02SQm5vrPHry8O23334ApeYNSK5tt90WgJtvvhnwJSuKhUruVq1aufU6leVYkuP6668HcKxc+qHfnzVrllsD999/f8A/H8VHxZblXcnLy6vQule1dgKDwWAwGKoBkmKeYgbr1q1zFogYmphE586dATj++OOBWJ1W+JSTcKauLB9ZyE2bNk1rrEIWniyyK664AsDFKUaMGOGyyeRbr6zaq3Bm4axZswAYNWoU4LPeHnnkEcf2lyyJHQwg1qOTCzTu++67L5D6+K2YwVNPPcXdd98NEFdAfe211wJw5513AjEWvLHGArIylRm6ZMkS56XQb6aDeYbj+WI6F198MUuXLgWgbdu2AOyxxx6At24FsaaZM2emtEZ46623BmIxVj13ZauHY4J63u3atePxxx8H4rPHpQt9+vQBYhnNEGOAu+yyC5A889Q4Llq0iMsvvxzAxTPF3sQWdMpQ8+bN6d27N+DXCenS0UcfDfh4oubvCy+84FhI3bp1S9xnMpCuzZs3D4DFixcDfh0JxrLFmCST1kd55sIZog0aNHBzRbH9cM18eaDriaHNnTvX/eaPP/4I+PwNeRm0tuXm5rpnrJp36Y4aqxx11FFAyeejTNxUMc+cnBzH1B988EHAs3wxeXk8zzzzTFcRoc9+/fXXgNcl6fo+++wDxNZOzdtE1kBjngaDwWAwJIgKMU9ZjIotjB492mUOKqtwq622AuCmm24CfJzq1ltvdTEKWW6KU/3www+AtygVq5NFlGrIYhUrUt2drClZTgsWLKBNmzZAPPMMN1kvDbpOspZ6VlaWsyBliZ155pmAt5jE4PLy8tyzUFxRjERWr+ppZakXFhbGeQEqAlnIYjrjxo1zmb161oqZqBZOFu2NN94Y16El3PlJevf0008D0Lp1a8co0uERCGcnauyVtbxs2TLH8hQTkmUuXRYT/vLLLwFo2bJlSmNDYjQHH3wwt912G+B1QUxAsSDFh8O1ekFIJj2vVGZQhr0n06dPZ/vttwf8mGo+KW4/Z84cAE444YS4OJfYariJ+QEHHADA8OHDHeuQZyZZPcnKynLr1R133AHg7kHPPhjH1PhddNFFgH9eygyWpyI4Nrq+rlcRmTUWWgPGjRvnPHrNmzcH/DPWui4WOXXqVMfwtP5pzHU9zUWNa9++fV1ms/5W0bVEY/bdd9+5mnvlZ6giIi8vz8kKsHz5crfOKidCeq771TgqP6F+/fpuPdJnyzPWCc2ISCRCTk6OCzSPHDkSiLVk0qZy5ZVXAj5YKzqsllrz5s1zm9YOO+wAeAou143+ns7knEgk4tKwNYiSQ+5Apef//PPPLv1cE1cuD7lqNDmFoqKiEu4P8AH5RBFsMKHJdtlll5WQddKkSYA3WtatW+cWark0ZcioiHn33XcHYosXxJIC1Bc1mcUl3Et31apVTiml/DNmzAC8a1GlJi1btowrYVKAX5NRbQanTJkCxBYiuchSuXlq09QGKNelNiUl21x44YUceOCBgE/KklGlDUsyKxlt9OjRtGzZssT1KwLdr363a9euLsFEi6JeZeBqfFevXu10RN8PG3jh8UyFq1n6rE186tSpnH/++YBfDLU4a5FU6CG4JoRbHwqao1rEv/vuu6QX8jAikYh7tloD5DaWXgTHThupXKTa2M844wzAl42pDGvOnDnO+JR7sSLGt3RYG/HUqVPdfJLRoaYpMlSk31OmTHHJbNr0tXnKcJXLulevXkDMzS/9SnasJfs777zjSpWkD5JVBEClYX369HFkQOud1hi507XGyVC799573f3ps+VZR8xtazAYDAZDgkiYedasWdNZsNrJd9xxR8eEBgwYAMQHwMVW582b53Z1FWDL3RFuhCw3Y7oYaNhdJitL7eqUOLRgwQK+++47AN5//33AMwhZXmJZspy32247Z+HJ/SBWXl4EGSfEkmseeOABwFtP999/P+ATRjR2RUVFLsgfttDffvttwJdRLF++HIhZascddxxAUi3YJIPcJDvuuKOzsOWeFZMX61fiyrHHHhtXPqEyBbnHxDjl3Tj11FMd00tVe77s7GznAZFuP/HEE4B33au0ad9993X3LDY1efJkwFvEClUo2WbPPfd0VnwybltdQ/pw1VVXObetksg0F8X+pefff/+900m5xbbYYgsgvolFKiF9lFzr1q1zHhQlfqhMTGUG0puFCxeWWYqj/2s85bZr2rRpShOFIDY+0lMl9oRDOKWxF81BtT0U9KyU5JKTk+OS6bQ+JnNKSTDZTsy8R48egGd4Gi8dClCrVi2n82orKVap0I/G9bDDDgNicyNZ5hl2Nb/44ovOs6NQh8ZPrF9JUKeddlrcuCs0NHz4cMDPZ82D4uLiCumFMU+DwWAwGBJEQswzGo1SUFBAv379AM+2+vbty8CBAwFvHYUTT8TImjVrxrfffgt4Zqk0fzElfVcxhXQd+yULTMF6WVwqrlb5TcOGDZ1FGGZzCvwr2UhxzQYNGsS1pEu02YMsKMVuWrRo4azdCRMmAD6ZQNZasCxFRfiyHmUl6n1dSzGxTTbZxN1fMpDc+r2xY8c6y1DNEXRPOlZKiTZPP/10XCKL2IjGXHGPk046CYgF/GXRpyrOsnr1aud50FiHjxVTEstDDz3kYodivvJUSB+kJ0pGa9iwYUrLafS7vXr1cvFLldIocUyMWaUel19+uWPGismKAalURIcHpPJ4wHBTlGg06uLu8oZoLirOLNnPPvtsN+6K1YVLmFTaoaP3jjvuuHI3ZE8E0lM1Gwk3pC8N4XuXDqt5iHIn6tWrR+vWrYHkGKfmouZ6r169XGme2P7KlSsB72kLegbE7OQ50jqje5YnRU0oCgoKkp6D+g3FaWfPnu1ajOpV3kHF91VSVVhY6H5fTFPrh/RBCVF6f5tttnEJT4notzFPg8FgMBgSRMLMs7Cw0BV+K6spGo3GMU5Blo9iMm3atHFxQlkA4YbEsuCUwZWOgvdoNOpikrJuFWMQQ1Q8qHbt2nTs2BGIL1sIx1mE0uIdiWaC6reU2Tt37lxXmiKLT9d85ZVXAJ8BXatWLRfHkgW7sXEsLi5OabaqxiQvL89ZucGYLPiG09KlL7/80t23Pqv/i92H76eoqChpazf8PCdOnOgYp6x2MTbFiJXenpWVFdecQZ+V9av/a56kWqeDZRpVTM4HAAAgAElEQVQ6DlBZ1WXhzjvvdAehq1xLc++8884DfHxckLcmFbLK+7Dbbru52Ldi98oeV5ma4mj9+vVzre5OP/10wJdJyIOlXAy9379//zLnaUURiUQco9f81BqhMdyQFydchpWfn++uq/dTyZLlLalbt66TT3Py1FNPBXxLVXmDtt12W7dGi2lKb+VJPOusswDPwlORcxB+VvXq1XP6oXyHCy+8EPCMszTPiNYNNYdR3FaeC8l60kknuVh/IhnNxjwNBoPBYEgQFap8Dlr85UWwCXx4d5clIGtMjFDxonQ1+ZZlp3q7sWPHAt5KC7aZCjduzgRkgSku1bhxY1cPphpUWejKAlYd5aBBg1ztYzIxk1RgQ4xW1p+KsNu3b18mO9DYp+PAa1mpilXeeuutLu6nGjDVASvWL72tWbOms8Qlo6xceVwydYB0NBp147cxL0J+fr7zugwbNgzwmYmvv/464OOlYkadO3dOevwll1jsBRdc4LK8FdvU8VtaK/TZ4cOHO4/QuHHjAB//UpN11Y+LmbZr1y5lTeyF7OxsN+eUm6F1KxGE2yGmC8GG+FoP5JnQ+ImJqr3dwQcf7DxaYm/ywugZdOrUKeXyh9fl66+/3jXM6du3L4DLuwkz+CA0F5V7Ia+dDnoXsrOzK6QfxjwNBoPBYEgQqT+1NISwlTl06FBnuSqeEm5erO4b4XZK6YIYXrhdWjoYTiKQHMp43HrrrV22mSxCxZ8V3wyOWSZZcrKoiDcjlQhnNg8ePNjFzJQRKY9E06ZNAa+nEF8PWRmeikSxfv161zZTR45dffXVJf4v74Xq6rp06ZKyeRHMyhZT13thJqBxbNKkiav3VRw0zE71queVDlaXlZXljk5UV5pdd921VNmrAoJrmsZYMWLFyOXVUhy8uLjYMTzln0jPxeZ0r6UdpJ2srOrMNmDAANcNSc8y3P1rQwiz03BWdNBbkwiMeRoMBoPBkCDSzjwFWQwdOnRwNX2qo5RloFdl3IUbhKcblXXMWFmQNaTst0gk4piA6vJUvybZK5stV1do/GSFX3rppS5OKWu6KrPIikL6oh7U0ivVHSqOqG5gOTk5KctYFRLJ8i4qKnLsR56isroHpXMuZGVlufVLcW3FhdUZpyognNncs2dPl0GrA64VC1QXn2Dnq3AeihDOo0hHLX5pHsBgbXBFr5eyo9JScpUEUFhY6BIxlGYcHvjwSRT/Vkhx1fw4Eom492SMpDvR4N+G4Ak4chulerOoipAeKSFESRWag6lskpAswjJUhkyRSMQV2YfPF61KCJd7nX766S7coHVYm7+edWku2Krw3KHqyAHmtjUYDAaDIWFknHlC5SeHVDeEj+gyZAZVycrNFDQnM1VaU12xfv16l0yj8omq6AUKhxxq1qzpjkUrq0wmXe1Q/2kw5mkwGAwGQ4KoFOZpMBgM1RkFBQWuNV34AIiqiHS1/fs3w5inwWAwGAwJIpJIXCcSiSwHlqRPnAqhVTQa3bSsP5rMKcMGZYbqKXd1lBmqp9wmc8pg+pE5lClzQpunwWAwGAwGc9saDAaDwZAwbPM0GAwGgyFB2OZpMBgMBkOCsM3TYDAYDIYEYZunwWAwGAwJwjZPg8FgMBgSREIdhpo0aRLVsTtVBfPnz1+xodohkzk12JjMAI0bN65yci9YsGCDcldHmaF66kh1HOvqOM5QPeWubjIntHnm5+fz5ptvpkaqFKFevXobLKrNz8/n7bffzpQ45UKdOnU2KvMbb7yRKXHKhfr162+0eDk/P5/XXnstA9KUH3l5eRsd6+omM6RGryORiDsbU8dQJVP3XR69fvXVV8t1LZ3lKwTPmEwlGjVqtFGZq9uaBzG5dW5nVUHdunX/UWNtbluDwWAwGBKENYY3GP5lUJPwdevWsWbNGsAfjBxmfJmGmOWPP/4IeMbZrFkzALKysv6VR8VlEsEjyco6nkzP4N/8LIx5GgwGg8GQIIx5/sMQPHoome8L/2bLsiJQDDE3NxeAwsJCwMcUKxOSTTLdcMMN/O9//wPgpJNOKvEqBpqp56/x+vjjjwE4/vjjAfjzzz8BuPbaawE45JBDqt2RWtFo1I2nji/TM9jQ+OqzmpPpvm/pR/AA7bLkk2xCKmLm1Q0p2Tyzs7PjJqYG8Z9wKnk0GnX3IaXRZJBbKazgxcXFGb33sFxBJQ7KVJ5rBJHpMwo3NNbBSQ0lda2y9axGjRoAfP755wA899xzAOy7774AdO7cGaicMx/DBtXEiRMBuPfee/ntt98AePDBBwHYZ599AGjVqhWQOXmlmzNmzABg9erVJd6///77Adh1112dC7eqbKIa3/A467VmzZq88847ALz33nsAnHjiiQDUrl27xGel89FolC+//BLwLuwePXqkRX6t3WvXrgVg/vz5QGzMf/755xKfkXv/nHPOAbw7fYsttnDyZ3ID1ZgHjVa9p/UhXXpibluDwWAwGBJEUsxTO/yKFSuchbLVVluV+Ft1RpA9i1ksX74cgPfffx/AWYey1P/zn/8AMQtIVnM6x0LurhUrVgDw+uuvA9C0aVM222wzAFq3bg3Es2VB7y9YsCCOMe28885pkx38GMtyrFOnjhuvH374AfBjLBdeixYtANhmm22AWOJLZXo6cnJy+PDDDwE477zzAGjYsCEAp59+OlC5bluxma+//hqAK6+8EoBu3bo5ff7ss88AeOCBBwAYOXIkUDrzTLVrPxKJsG7dOgCeeuopAI444ggAdtxxRwDOOOMMAF566SXH2spCuPwmXdDvTJkyBcCtgSeccAJQcr698sorgHc/qxTtvvvuAyAvLw/AJXBNnz6diy66CIC///4bgBdeeCElcksf9Pr7778DcNVVVwEwYcIEAAoKCuKev+5ZJUe1atUCcPfXvn37jHoENMbyVHz88cfu3126dAFg001jZZqpTnIy5mkwGAwGQ4KoEPOUxSJL68QTT+SXX34BfKynZcuWQPmsvzBrCAfKwfut08kwwtcOJn08+uijADz55JMAzJ49G/CxLsULLrzwQiAWE9Df0hEDkGxiE1dffTUA06ZNA2KxCVlcvXr1KvEZxS0UE9D9FhQU8O233wJwyy23ALG4WCoRHmNZrj/99BMQi8ctW7YMgEWLFgE+TvTHH38A0KFDBwCGDRsGwGGHHVYpjFPPYPny5U6Wjz76CIDJkycDnlFIf4PxW41/uqGxkVdCsgwZMoRPPvkE8KyjLJmCc1OWvVhIzZo1k5ZPz3zVqlUAtG3bFoD99tsP8OzuwQcfZODAgQA0atQIiPdeiE03adLE/T0dc1CsTHNu6tSpAOyyyy6AZz6FhYUutiwZNe4ab3mOFEvU+gJw1llnATFWV1EE47FLly4F/JqlOf/MM8+UkCk3N9fpeBj6jK5x5513AnDFFVe455KOeLnuQzqnBid33XUXEJt/Gst+/fqV+Fv9+vVLlSsSicStH+XZt4x5GgwGg8GQIJKKecqCXbp0qbNmXn75ZQBOO+00IMZmykLYYpRVLstR1/rqq6+cRdagQQMgtfGMspjvwoULgRgLk49f1uQdd9wBxOJG4BnpY489BkCfPn0c49vQGCQKjZXiILL4ZJmLyWVlZblnojiWvqu4S506dQA/lj169GDlypWAj4t99913KZE7/Kw1xuPHjwfg+uuvd78nr8WBBx4IxKxZiMVkwY/9BRdcAMTii2IosoTTAVm70hON71VXXeVa5SnGGY4Va648/fTTAMyaNcvds9hpqmN0kvOvv/4CvK7stNNOAPTt29eVhpTl0QnPiffff5/zzz8fgOOOOw7w91xR5OTkOAah32nXrh3gx/zMM88EYiUst912GwA33XQTgIuXPvLIIyXu87DDDgNi8VJltaZj3dA1xZpnzpwJ+LUiCN2f1gQxfmXjSqf69evn5uDWW28NpMbblpWVxeWXXw74uKvYpfREMq5fvz6OsWuN1jwW7rnnHgC6du3q1n6tUalg/WFvoOK/5557LgA9e/YEYuxZ2ckqu9LYKpNczFPXys3Ndd4UoTzNQox5GgwGg8GQICrEPGVpNW3aFIC9997b+ZVlyQbrlaB0qylcMCz2dvfdd5e4VnFxMUcddRTgsxhTYUGGZZO1IZYpZrNixQpnrR1++OGAj6fou7LCJ02aBMTiCH369ElaxjAko2IiYpyKr+6xxx5AzNpWHFFsWCxPVqOy+erVqwfEGOrtt98O+IxWsaJkEI1GS1iz4OsKFYfdYYcdgFimomJaek+Zn2IcklesJN11ZdI1Na3+6quvAJ8p+eeffzq2LBYkFqJMxrFjxwL+ebVu3dqx5HTFa2VZz5kzB/AenQMOOACIeXHCdcqC/q97172OGTPGxe+UWZ9sbCsSibhrKkNcMU+xF+nCkCFDHLPcdtttAe8dUV6CPit20rRpU9d0IZXMs6x6ZNX0CllZWXGMTXqhmlvpz+jRowE45phjnH6Xt057QzLqd1esWMGSJbFe54ozB71V4NeSFi1aOB3SHFNui+QPN1ZYvHixmwOpQiQScWOs+LLiwEcffTTgvVObbLKJWx+0P/3666+Af066J2WYT58+3a2ne+65JwCDBw/eqFzGPA0Gg8FgSBAVYp6yQhQzU3wC4JtvvgG8ZVIaO5AVJh+7WKtiWf379wdw8TcxqGRQGgMOt1KT5apYlHDTTTc5C0dWtl6VYSdrWJle6UBQdtVAaoyUWat6uD333NNZqsr+23///QEfGxKzr1u3LhCLDcjK1WfVOaQiCMY5ZfWJgd1www1AzMIGGD58OBCzduWJEAseN24c4OND06dPL3HP/fv3T0usU3ohpikZlQUsln/++efz0EMPAT7bXDWpX3zxBeBZ3ymnnALE4jHyoqQ6KzHciUk1eHoesq6D3WD0qnvW85Jea+x79+7tajDV8SbZrOHSOkSFvQmKER599NGupaA8J6pjVozwoIMOAnzG+LPPPuvYtjIuk2WgkUjEzRXF2DRm0ksxuBUrVriuPVpzdD+qVRbj1FyNRqMpzcaWLNOmTXO5HFq/w93R5HW644473NgK8sA9++yzgF/Lda0JEyZw8sknA9CmTRsgef2IRCJufksPlVNwzTXXACVjsIsXLwZ8NYiehzwU8qJo7V66dCkDBgwAfJy6PLWqSW2eQtu2bZ17TxudFneVFUiYGjVqxBVrK6B78cUXA7H+lQCDBg0CYjeXikJsKOlm0EKhzfvGG28E/OKixJpmzZo5BdCrXMtyJcpIaN68ORAL8qezWFjjoQVSm1zXrl2B2OKtz8glpMShSy65BIglrYBfMLfYYguXDKJNrSIuxbChkpWV5Sabxmvo0KGAbyoQXGjk+r755psBuPTSS4FYazbwyi9DITs7u0z3YzLQ89PYKilChexK5GjWrJlzVf33v/8F/AYvF6J0S/cQjUbT1zYs4KIDP7900PB2220HlFzUNG5y5WlRkiGpex05cqRLktM9p2JultUbNewaLSgocG45ucblJj300EMBv6DLuJkyZYozMlOZcKgNUJuRrq01UAmP119/PXPnzi3xXW2SWkdEQMrT87Yi0DiuWrXKucJlSJT1W8H3w8lRmUR2drYrs9Jz1NqgRDCN2+zZs51RpXkql650W0arQoFHHnmkazMY7km9IZjb1mAwGAyGBFEh5hluvNulSxeXPKCCdiXdyC0hZvDxxx+7shO5O+RekbtFbjLR7hYtWsQ1UE4UslxlDc6cOdOxHTUCOPLIIwHPjvSd4uJiZ83LZaSEFzVFkGUk675Lly5pKYIPN6EWxHzVACFYHqN/iwWJVagoWm6a7t27O3dIOGGkIjJKpmnTprlnLve3krHC158yZQpnn3024J+Hkj1GjRoF+OL43r17AzE9TGfTDFmj0vFwadV7773nkrLUyEFjqobmYq+pTqYoDZJLxe9qHSiXsZhbUVFRXOhCSTZyk6kwXwypa9euKXeRFxcXO8u/rMMAlKhy9dVXOxe4SsFUJqQ2jnpOHTt2BGJuXTWvCIaYkkV4LioMpYYZYj6rVq1ySTn6rDw8Gt9M6AWULMEoqwzl+++/B2ING8JNEsTews9HYYozzzzTuXpT5VnJycnhxRdfBHySmLwnkkctBceNG+f0XjIqCU1tExUW1NgXFha6dSiRNduYp8FgMBgMCSKpJgliky1atGDvvfcGPPO87rrrAG+J67OPP/64i/soGSF8XJMKVmW59ezZ08VUK8o8ww0C3n33XWftihXpNdwecNWqVYwYMQLwR06JnSoNWpaLGFUwjpNKViQLVXEsXVvxndLGR++JgYpdKnYl6zISibjPJBPb0FgreeyWW25xrbKUcBCOoWjMJ0+e7Ir4FW9TDEnJOIqBitmmu82dxlieCump4pvDhw93bEzp8fqsxjaVjTI2Bo2t5pHGJ9zkIRqNus+E2VOnTp0AzziVHJSOxKzi4mLXAF5JYkqgUTKbmNtbb73lPCbyRilHQjFpzU2tGW3btnXJIWId5SmC3xg0zuF8CDEfxdZ23nlnx/6lH4ohZ6qJun7njz/+KHM9CnsUFy1atNEmCfq79L1du3bu34qtJotIJOK8DUoGUl6EGlIoKa5evXrOY6WkR62NKi/UWCSry8Y8DQaDwWBIEEmZX0HLS22SZLUoDqHyD/mqr7jiCmcpytIRm5JVo4yqYExVmWEVtdTEFvTbu+yyiyvGVzODcNq+rJ3hw4e7GK5iWJJDWZS33norQIli+XTG4RRjUIq4mF15INnDlmbKjur5f6tU2bB//fWXSzFXRqKeuRinYlqrVq1ybdUUN1Tmr9LIZVHqmabrMGxZ0GKNyk7Wq5p6NGrUyGVsK8NVjE4x6EweEKznKZ2VLMoxENsvKChwMU7JJ0ak8qDu3bsD6W17WFxc7LLU5RVRiY9yJp544gkg5nUIH3uoNmxirWoGokL6jh07upiZvBg6QjAZSM9VkiF9EcMRA9p0003duhOO6aYb+h15ge699163ZgjSl3DrzPLIKL2QF2u//fZLWRZ2UD41LVA8WXNSrFJr+Xbbbedi3fK0aJ2QrHYkmcFgMBgMlYSUHIZdXFzsYhKKDcrCU7MEMbK8vLy4hsFh1iCrQhmKffv2jWvllyjTkPWhLLdgTDJ83JksSN3DG2+84QptdQi2miqrcF5x3HRnzUlmMbUtt9wS8CytPFZVqg+FDUNjrXqr5s2buyxkjU84U1F6UlBQ4FiImmYok1mNCJQtmo72dsH4pjKrFS8T45RHQoznnHPOcTIHj3MK/r8yEI6z6j4aN27s3tO9KENSMXsxzkzEaqPRqFs/lFGtzFm1ZlRd5MEHHxzXrk5F+SqCVzb5p59+CsSO/5LnamO1jYnILGbz8MMPAz4GK++KYq6vvPKK0yutfcoFkd6kG5p3q1evduMneVVPr1pU6cTatWvLbOChsddcHDJkCBDTrVQ3/Vi/fr3LrFe8W/kqep7BvUj3l27dNeZpMBgMBkOCSInjvbQOIbIMZFnJGvnrr7/KrFWUxaDjZZRtuc022zgroqIsIxzf29BnJKvY0gEHHOCsWsUa1bVCsoat4XQ1+1ZcQlat2Fe4EX9lQmOw++67A7Hx3BgDkxVco0YNTjzxRMBnWsqbodh0Ohmnnv348eMd69HfFNfffvvtgZLZyuH7q0zGKR1RBqvq3NR8XS0Si4qKHOMTc1CXnsqSX3qgulm1kFRD8AYNGsTJpvtV5yx5rHT8W0FBgdMhse5UZLlKLxQnDmeQ67VVq1aOoal2XTFIfTdd0H0qxvvuu+86j47WaHX5kn6ocfx9993nWKjWF0Hr8bHHHgv4+G5RUVHK16BoNOqesWozNU/DupDJ9c+Yp8FgMBgMCSJlKV9hFhBuoF7W54KQ1SArTc2cgx0g0sXogpDMypRUzVnw98OWz4aOXksHwkyzKjBOIZxFHXwvDI2j2FH37t1dJyTFkffaay8gvTVxsmzVk3n8+PH07dsX8Na1MkGVhSh5KpNllgbpgmJZb731FuAzxYNZ8qp71JF6GodUx602hnBMUAxNfaaVYVtaToFkDbNodSwLxtHToUNlPX/dU8uWLV21gXoeZ2o907OWzrZr187VwYZ/W2MUznzeEMKdyNK1DoVraqsCMpMvXU6EH2ZpjaszKUciDyyT8oF3XcrQCLfRqi4Iu7qGDh3qEi6UuKV7TeeCowVYRewTJ050rnGNsVxVmSpsryjCjSfkslTpRrABhgr55SLP9KYpSCYl4ajxt/5fnuQP6ZKej5L8giegZBLBBESFeYIlWcHPZEqWoqKiuPWtrGb8G8LGrvFvgLltDQaDwWBIEFWKeRo2Dll8SlpRe8Bwu6zqgrDbp0GDBu7fcuGVlWCWDsi9tfnmm8e1NaxukPxi0MESFUFjXVmMsyzIjZ/MUVhV5Z7Wr1/vQhFKfJI3pTIZcUX/Xt7P/NNhzNNgMBgMhgRhzLMaIdiGTkkRglpuVcZhtalAaUegZTqOHERVYS2pQLh0ojrgnzT+EJ+EmMpDuQ2VA2OeBoPBYDAkiEgivutIJLIcWJI+cSqEVtFodNOy/mgypwwblBmqp9zVUWaonnKbzCmD6UfmUKbMCW2eBoPBYDAYzG1rMBgMBkPCsM3TYDAYDIYEYZunwWAwGAwJwjZPg8FgMBgShG2eBoPBYDAkCNs8DQaDwWBIEAl1GGrSpElUB0RXFcyfP3/FhmqHTObUYGMyQ/WUuzrKDNVTbpM5NSiPfjRu3LjKyb1gwYINyl3dZE5o88zPz3dnA1YV1K1bd4NFtfn5+bz99tuZEqdcqFOnzkZlrm7jDDG533zzzUyIU27Uq1dvo2Nd3WSG6il3ddTr/Px83njjjUyJUy7Ur1+/XPrx+uuvZ0KccqNBgwYbHetZs2ZlSpxyoWHDhmXKbL1ty4FIJOJOLUn3oa/JQmc4ZmVllTjDDypX5nCf2qo6fqmG7lvPRSgqKvrXjIHB8E+ExTwNBoPBYEgQxjw3ALGGdevWsWbNGsCfiqBzHysLYi2SQ8zmxx9/BGLnfNaqVQuAli1bApCbmwtk/gzBIAsuLCwsIcs/lX3JU6H7/fbbbwGvU5tvvjk1atQA/rljYDD8k2HM02AwGAyGBGHMsxSEWcMNN9zA//73PwBOOumkEq9ifplmD2Ity5YtA2DGjBkAjB49GoBvvvnG3ceZZ54JwBlnnAHEWA+k/yxB/f6KFSsYP348AH/88QcAZ511FgCbbbYZ8M85v1HMUvdz++23A3DTTTcBXl8OPfRQrrnmGsDOdkwX9CwikYibn1WF5Wtu1KxZE/DPvqCgAKg6cv6TIf3IysqKywspz1nClbp5liVgZSmO5NHvT5w4EYB7772X3377DYAHH3wQgH322QeAVq1aAZlZ/CORiHN3fvnllwBcfPHFAMycOROAvn37ArHF+oMPPgBwG9cvv/wCwH333Zd2WQHnNn7llVe46qqrAOjSpQsAJ598MhCvA7m5ue49GS/VaSHR5qis0ltvvRXw97B27Vr393Xr1gGpPfQ7Eok4w0rQghzenIOhh3+C8aINSfelsQ6GMOrVq5cxefQcsrKyXKhEevDFF18AcP311wPQqVMnAM477zwgdg+Z1nuFfqSP5Qnv6DuVrT/B8JXmVXgj1P8ls/Rj4cKFbL311oAPy5Vn7M1tazAYDAZDgsg48wyyJ1mKsoxlEchCzrQ1o9//+uuvAbjyyisB6NatG8uXLwfgs88+A+CBBx4AYOTIkWXKmqryDI1TVlYWS5bEyo7OPfdcwDOcc845B/BMtEGDBgwYMACANm3aAHDZZZcB3sUr9ixLLdXQ/f/+++/ume6www4AtG3bFvDWrf7+zjvvuPsVS60OiTVha/3ee+8F4O+//wb8PehzP/30Ex999BEAzZo1S9nvr1mzhk8++QSAlStXAvDee+8BsGrVKsCPY+vWrTn88MMBaN68OVA9XcdaT/78808AXnvtNQAee+wxAF599VV23nlnAF544QXAezVSibDHROP+66+/OmbZrl07wK95HTt2BGDSpEkANGzYEPCemXRC8oq1KSlSIao5c+aUmRgpPd99990B2H///YH0rSVCuGRQ+Oqrr4DYvOrZsycQv/7qu5oXCmfNmjWLd955B/DjXx7WbczTYDAYDIYEkTbmqV0+7EcvKChwHTvUTeL7778HoFGjRgAMHjwY8OwkHVZiaZCM6swh62PIkCHOmlfsriyZgkXxq1evBuKTA8oLfU/XufXWW92Y5eXlAXD//fcDsQQU8Kxi3bp1TpZDDjkEgLvuugvwVu4ee+xRQuZUMztZh82aNXPyhvVB/1+6dCkQY85KgrrlllsAb9VmSg+EsIzSh7D1G4zTPvnkk4Bn92HLPchOVqxYkTJZxWw/+OADjjnmGCDGeMDrXZhpRKNRNt001nnshBNOADwjqg7QPX/66acAjBkzBoCnnnoK8PfdsWNHp1Pp9F5IL/766y8AlxD22muvOYZ/2223AbDddtuVeJ0zZw7g5+Yhhxzi5kwqvQFBz5+Y5uOPPw54xqnOVatXry4zHi+Z9B19bu+9907ZGJeWvPPdd98BvvxO3gZ5CWfMmMFDDz0EwKBBgwC/bkjvH3nkESCWiwGxOHhFSg+NeRoMBoPBkCBSwjyzsrKcdSBrUNmpyvCUdTNjxgyXKSqIceqz8+bNA3yW6GabbZbWWIxkl8V45513ArDTTjsBsQzWjz/+GCg7lTnMUt5//33OP/98AI477jgATj/99ITk0rV+/vlnIFYy06dPH8BbT2EffdDq079lge+6666AtxYXL14MwFZbbQWkntkpDty8eXNnRcvLIOgeFVP+448/+OmnnwCch6J///6At+zDWXPRaDSt+qHYlTJnlbEpHR80aJDTlWeeeQbwVr3GPmyN16xZk+7du6dMRjHGnj17st9++wG4bGvNSemIrPdIJFJmqVWYpQYzWZbS2DQAACAASURBVJWlmM6cBP1eMGNV0O++9NJLAAwbNgzwGeiaZyonu+OOO1xMK52QXFrPzj77bADat2/v9EIyH3/88YCPidepUwfwelNcXJzyLGxBvb7vuOMOgLh+sh06dABicddtt93WyQN+zn3++eeA9w7pXkePHs3BBx8MJL+eBNdU5Zho3ZOXQcy9cePGQGwevP/++wAceOCBJa6jsQ73/L3wwgtp3bo1kFgDGWOeBoPBYDAkiKSYZ7CeSru6LDwxTWW+KdMvPz/fWSZbbLEF4AvnJ0+eDMDcuXMBb6WddNJJaY3FKAaguINY0AEHHADEMldlVZbFOGWZqYZyzJgxjpmI2SVqqevzikvdc889LmtQTK481p1YhWpSFWvTuAet+nQgNzc3jjVKbtXfKT63Zs0ax9ZkTQYZZvBVDLVevXrUrVu3xN+SRU5OjtNdeQ6kw9JFPfuZM2fGxXJ1D2Kpel/x6+Li4rhm8clA912jRg2X6StIv5WRKMabm5sb50mRTHo++o5ihp999pnL0tbxUalk/eG44fTp0wHvfWnUqJGTRY0npMdXX301EGMSAE8//TQQi0NrLqeSzZUl+/z584FYljnE1q9p06YBPj4rHdJ9aq1Q05BGjRqlZFzD69MjjzzCjTfeCPh4ofRBTF1elPz8/DKbS/To0QPwjFnZwTNmzHD6kWyWvL7/zjvvuFix5qDm/m677Qbg1sVJkya5fSnYJAM8q9eY165dG4hVI+g7iazRxjwNBoPBYEgQFWKesqo//PBDIGbxiTmodk2W63/+8x8ADjvsMAA6d+7sdnfFBBXjDB/3Jd/84MGD08I8w63UlH2l399zzz2BmDUetsBkzctSV5xU2bi9e/fmiCOOALyVlmgMQOOhrheDBw92PvmKNHfX9VQ/KSaarkbxum6bNm3cb6lxvbJrlVEthrFq1SpnBaqNoCxQ1ZBpHFXbWqtWLW6++WYgde3+cnNzefbZZwHPChTLuuCCCwDP4CdNmuRqx8KZyxqDMKPbYYcdEupmUl5Eo9Eyn6dilUIkEnGMXbrxww8/AJ7FaY6LRX377bcu3qWYWSoYkuaTmNmIESMAz+LE6v7880/HHMSclFUpdinmrRrs3r17M2rUKCC9cVrprbxP0tdDDz3UyabY51FHHQX4Om3VjytDNycnJyVrXvjAiFGjRjl901o1cOBAAFq0aAH4MdrQ7+uZ9+7dG/C1yi+//LLzElQkjhiEvjdjxgy3XnTt2hXwHZn0GclcXFzsYvqaaxoDrQ1ixspleOqppxyDFZMuj04ntHkqzXn27NkAnHjiiQAsWrTIuRH79esH+KC9No5gD0e5wRTYnTBhAuA3S5VUaEFKF4K9V8G7nOWOUjA6uOlpcZTrSMquNltq8zRy5Ei6desGENcuKlGEW7tV9PtyGar0Q4XxcrmnGlLAvLw8rrjiCsAvGlOnTgX8Rv78888DsUVU4y33vQwv6ZBeVXA+duxYp3cquajoIqlFfMGCBU7PNUGVrKVSKm1+zZs3dw0owptm0E0bRK9evVyyV6YaE7z88ssl/l+jRg332ypn0hwIu6Y1V2rVquV0P1WIRCJuc5ZB/c033wDw8MMPA173hwwZ4mRSYos2WC3k2sR22WUXIJbopdKGdBjh+j3JoVfpRL169VyCkJJzjjzySMC7Evfee2/Al5ylKnlP80Dr8wUXXOBaA6qJhDY5rXvlGaPwqU6dO3cGYsZAsvosXZOL9t1333VzXmVY7du3B7xhK70tKipyei7jQPuUDHi5p5U4OXXqVC6//HLA61R57sHctgaDwWAwJIgKMU+lwCux5sADD3S7udy04XZlep03b54rQZA1tOOOOwK4tkqyzuQmS1dhs6wmnbUoF9Upp5wC+GSPoqIiZw2JmajNlyxiWUJ33303EHMvVJQpphqyJOWmEPvLFOMpKipybcjkHpFLTexLYxWNRt1Yy4Un9qbkIj03NXmYMGGCK4wW86wo5CJ+9913nYUut49klQ4oUWXOnDlOvyWb2idKh6RbvXr1AmKuo3DzhVRDc1Dy6vnr/bVr17p5G054CifWyHuy6667upN7UuUCzcnJcfNpwYIFgJ9HYvdqmL5mzRqXPKL1QiUqcu3J/ahWkJtuumlaEw71zCW79Fe///fffzsPy3XXXQf4AybkzRCjCp+ykiy0dio5ZtiwYa60R54/JTPpUIlwm9TSIDnHjRsH+MTQQw891IVbKqofYeb5wQcfOA+m1i7JqLVbe0rTpk3ddRRWePXVVwHYZpttAM8upVsVhTFPg8FgMBgSRELMs7i4mL///tv57xV4bdy4sWOJQQYRhCzZX375xVnssuTFZJWIoBikYnPpsszDsUDFGcLtzKLRqPtMuKGCAteylGUhVQXWGWzMDl4mscBwswFIT0JFNBp1z1rlBfI6iJEp3rLLLru4RB2NeVllQorZNmrUKOXjvW7dOqcPstpVMqTC8EcffRTwZRTg0/yHDh0KeB2XzuvszqKiInf9VJdPhMsTnnvuOcC3XQs+b1nfSpRQ3PDUU08FPPuXrIcffjj169d395AMxDB+/fVXF9sUExNLENNQQ48RI0a4RDx9X16f8H0nk1yXCPR7OrRBYxpkYJJNDT/UsESeCd1Lug/D+PPPP92YinGqpEclhPLoFBYWxumovD9K8lS+irwb+++/v9OPZOdkMG9Ac116qqY1F110EeATokaOHOlKb+655x7AewRUCim5wt6WRGHM02AwGAyGBJFwqUo0GnXWh466EiPdEGRRdenSxbFUWezKppRVoViGMijTZTnKqpJPXExHVkzwdHfFZMTWlFUrn7+sncpinKVZT3pOSt2WRbjlllsCfvyDxwgpZpDqxgl6hmJvikeEkZWV5WJWig+J4Q0fPryEbLIov//+e8f4UoXSxlPMTTE2ZfplZWU5dqpjjpo0aQJ4fZBuB8c6HQX7kUjEjbVKapTZrDkazIJWVrzmmjwpiuNpXINlXaliR8Fm9opdKWtTeQfSXZWunHPOOXGNNjJ9YIAQbp8pD5r0Nxg7DHviNBf1fqaOXwzmH6iZhLKCFadXJvDRRx8dV26iTOJLL70UwB2YoSzhnXbaKWXxZelHkyZN3O9ccsklgC9tk37IG3HkkUe6khTprkqaVM2h8iDNzUWLFlUoxmzM02AwGAyGBFGhJgnapRPZrWVhbbbZZtx+++0APPHEE4A/Xka1TmJGmToEOWwpyVJXezjwmcWyxGTVi3Fm6ignMYJw0b1+X/8vLi52lpbuZ9GiRYDP7JO1r+/Wr1/ftVVUjCHVFvHGdCc7O5uDDjoI8A2cVfergn55LtQsOisry2Vsp1pO8GOuOE/4EISCggIXq1NWpca0rPZm6YR+W94SxVsFxdsuu+wyV8ssZpxJNicPwo8//ujm15QpUwDP5lR/qqzgdB8CkAg0BxXrVIMY6euGUJn3oDmtY9L0rFUXqdeZM2e6+Kfa4amRjHRM66Bi5Hl5eUmvGfq+2reee+65Ls9AzSS0Fpx11llArP4XYixVjFLzVJ/dd999AR931vObNm1aXLOQ8sCYp8FgMBgMCSJth2GHEWxAPWDAAKBk+zvwlrwsj3RnycnyFWuRr1yxrLFjxzp5FD+UhZPqTiDlQXZ2NgsXLgR8rEEZyvLjK+4SiUTiMp8Vo9a9qGG9LLS+ffs6VldZlnFRUZGTQfFDZQvfcMMNgLd6g0etiZkkK7fGqk6dOmUe16Xf12+1bduWa6+9FohvcZZpRKNRF09TzFh6vNdeewFed3v06OF0pDLihhrHHj16uJpIHc6gdm9ixMrAV3ZqVYD0IpyRrMzxTHobEkFYrmOPPRaIrxyYP3++y8TVnJRnRTFG1fVrTUmFHmleaX0+++yznWdHMU51C9KRafpsYWFhXC6B7jeYbxD8nT322CPugPvywJinwWAwGAwJImPMU4hGo3ENe4WwZZAJWcA3lhZ7u//++0v8vbCw0PnJ1Zc3U3VZ4GuoPv74Y3f0j+qc1D9XcSx1CQlaUGL0Yvqq5QtboOvXr3fPpjKtZsmgmll1Y1EXEcXHlNHas2fPpLuaCNLB/v37O4amZt4aR8Vk1aS6c+fOLhZeWYwzCD176bW6GqkeUs9WtcqVBXmWttpqK5d9rR6lynsQ49BaURXGV5AsOuBdnWvkwaqqzFMIZ/rKA6cOTsGD65WXojknr4G+m0rPRfhwBYDtt98e8OuddDzYED743fKgtDr3RJDxzTOIylau8OnoSodXEDq4AanYXYHlTE5iLTJbbLEFEydOBPxCrqJ7uVXKowiVvWiWF5qQStzSZhY+g3L9+vUpex4a62Bim9Ly9XvaqFUMX1RUFHciUGVCssjFKR2prJKOjaGwsNAlLoUXx2ACXFVCsCRI5Rva8OU2r2oybwwaa8mvRhXg17vKWjv0+1XJeDK3rcFgMBgMCaJSmWdVgdiCWsYFS1SEsJsgk5B89evXdzKG/xa21P9JyKTVGWSzYm5KrAqPdabKkyqK8PFoVRmV3fAgUQQPMFA5jTwRCrNUN+YpVKQU8d8IY54Gg8FgMCQIY54BVHWLKxqNVgsW8U9BVdcHQ9WAGq2L6Vd1j4QhNTDmaTAYDAZDgogkkh0YiUSWA0vSJ06F0CoajW5a1h9N5pRhgzJD9ZS7OsoM1VNukzllMP3IHMqUOaHN02AwGAwGg7ltDQaDwWBIGLZ5GgwGg8GQIGzzNBgMBoMhQdjmaTAYDAZDgrDN02AwGAyGBJFQk4QmTZpEdY5aVcG8efNWbCj9uXHjxlGdr1dVsGDBgg3K3KRJkyon8/z58zcoM1RPuaujzGB6nSqURz+q25oH1Vc/qtNYJ7R5tmrVyh0ZVFVQq1atDdYF5efn8+qrr2ZKnHKhUaNGG5X5zTffzJQ45UK9evU2Wn+Vn5/P22+/nQlxyo06depsdKyrm8wQk/u1117LgDTlR15e3j9Or6vjmgexsX799dczIU650aBBg42OdVWbi7Vr1y5TZmvPZ6gUqKm2GrFXpaOGUgndX/iMQquvNlRHaN7qNXwm6L8JFvM0GAwGgyFBGPM0VApWrVoF+MN1mzVrVpnipBxhy1zNwnWIefBvBkNVRU5OTolXzduVK1cC/sD1TTeNhQX/TU3xjXkaDAaDwZAgjHluAIpTgbGEZBGO/d10000ALhnjjTfeAKrHwc0bQnZ2NuAPdb7//vsBmDdvHgD7778/AIMGDar291rZCM7P0lAV56xklp4oVliVZJXXpGbNmnzyyScAzJgxA4B3330XgLfeeguA9u3bA3DOOecA0L9//ypzL2H9SLVctnkGoMGuWbMm4BW7sLCQWrVquX8H/2ZIDDob8+effwa8G2hjC2FVhxZDTdBbb70VgNtuuw2A1atXA/Dee+8B0Lx5c3r06AHAunXrMiqrkJWVVe0SP3Jzc92/165dC8Sft6rPyNVYFYwU6Yf0YMGCBQDstNNOgHfnV+bZsVr3Fi9eDMAzzzzDc889B+A2UemLxnbOnDmAn8ft27dn6623BvxamUnk5ua6Mfzzzz8Br9t169Yt8f9kN1Nz2xoMBoPBkCCMeeKtKFksqjX68MMPgZiVeNBBBwGw3XbbAdCoUSOg6lvqpUGWuV513+vWrUuby0UW6y+//ALAjz/+CHhrtzojKyvLWbl33XUX4Jmn9KN27dqAt4bXrFmTcbYt9iOWs3z5cn777TcA6tevD0CDBg2AquMJCHuDFi9e7OblY489BsCKFSsAzyS23357AAYPHgzE2FBlztPs7GymT58OwMiRIwHvxt91110BGDNmDACdOnUCMsuWtQ4odHL99dcDMHv2bCeHPqNxrFOnTon3v/rqKwBeeeUVdw+ZQFhPFy1axLPPPgvAhAkTAPj9998BuOqqqwA4+eSTS3ynorphzNNgMBgMhgSRFPPUri/mFoR288r04W8MknvZsmWAj089/PDDgLfQu3TpwqGHHgrANddcA8DZZ58N+PurKkFyISsryz0fsT7Jqs40H3zwAeDTzAcMGEDDhg1LfDaV8gD88ccfAPz666+AZ/JVDZFIxDG18DMOP+saNWo4q/3mm28u8R1dQ/G5du3aAdCtW7e0xISCcuv5S5ZFixYB8MILLwDw+uuvOw9A8+bNAbj33nsB2HzzzYHMe1bCa4qY+uOPPw7EErC+/PJLwI+pklaUl6AkreXLlwMxb4CYfybXI+n8smXLuPTSSwH49ttvAdx6ovt64oknALj66qszJp/Y/MKFCwGf9PP1118DMb3ed999Adyr4vOax/K0KOb5999/Z0L0uNjrU089BcCoUaP44osvSnxGEPNUOc1RRx0FxLwuFVm/jXkaDAaDwZAgKsQ8tdsvXboUgNNOO81ZMXvttRcAJ554IuBjKUJhYWGVYKNBC13W3z333APgsiDl++/QoQPDhw8HcLGLo48+GoC8vDyg6sQ+ZW2tXLnSWYHvv/8+AI888ggAc+fOBTwrUszo7rvv5vTTTwe8xZ9q6NkrliKGUxXx008/AT4OuKH4rMZLrz179gQ809D97r777kBMb1LJPMXY1qxZww8//AD4uNqsWbMAH5fS/fTt2xc1D1fp0EsvvQTASSedBHi9ll7l5ua691IZlwuzBK0tV1xxBYDrT7355pu7tUXxwu7duwOe9cgr9PLLLwPw5ptvOuYktpoJ6JmsXLmSb775BoA999wTgCFDhgCeMcn7pbFNZ8xZ6/eSJbG2rSNGjAA845R+XHLJJRx//PGAz/HQc9J3Jb+aJrRu3TptckN81vJ1110HeOa+YsUKN0/DYxiOfaoJ/b777luhuWjM02AwGAyGBJGSmOfy5cudVStWo/qf4447DvBtnLbddlvHRmW5lqdwONUxxaysLD766CMARo8eDXjWLIYmCyw3N9fFKI444gjAWzGyyDbEpjMRDw0WNgPceOONTJs2DfDxxRYtWgBw+eWXA/6ZnHbaaUB66w0ln2RRrE1Ze1UFinN/9tlnjuHssMMOAFx44YWAt1iD+itrXvcphiOLVmMvPSoqKkqpXkjuDz74wOmzvCLSY2Uftm3b1n1PsUCxU2WwnnLKKSWuq5jWhx9+6GLkijVW9D6CMXmN5ZNPPgnADTfcAPhYrHINDj/8cKcz+l1dR3E4xT6la0uWLHFrS2VBMqoGUvFY3XebNm0AzwrT5cmKRCKOoSsOK1avcb344ouB2LoQ9GiA14fvvvsO8F4rrYMtW7ZMy3qnrF5lh8sjMX78+BKfq1mzZpmsXTog75AatAwaNMiYp8FgMBgMmUCFmKesos022wyAp59+2sVMpkyZAsDzzz8P4M7vk+VwxBFHcOqppwI+y1NWjVo+9evXD/AdISKRSMrbWNWoUcNlislSOfLIIwFvqYuJ5ebmOibRrVu3Evce7kak72RnZztLJx2dTiSzxlUxB7HmCRMmuLES01R2WcuWLQFvYer/PXr0SFtXEMmr8ZH1q5q8ZBFmFonqieTT/U+aNMl5JrbYYgsg3sug7xQUFDB//nzAM8/PP/+8hBzSabG1SCSS0kxtZRB269bNxfBlWSt7vEmTJkBJz47uQaxDTFQxOl3jwQcfBGKMXHHbiRMnAonrdTgL/LXXXmPSpEmAZzT77bcfAOeffz4ATZs2dbKHm4/rOptssgng1xXNzXr16iU1xllZWXFesUTyNrKzs90aoPHUWZvywvXp0wdIP/PMzc3l0UcfBWI1meDHTzoqj0tpcmi9+fjjjwGvJ8oTadWqVcplz8nJcbW92mdefPHFUj9bXFy8US+D7lcsuqK6UaHNUz8mIdq0acMdd9wB+ESa2bNnAzB16lTAp0OPGTOGhx56CIA99tgDgC233BLwyQr6u9xlW265pWtSoAmRbNJRVlaWS0rQotKxY8cS96fB/f777517QBNX5R5yfcpI0GvTpk1d8FzF2nJBJSs3+M1i5syZgHdryV3eqFEjOnfuDMT6TYI3UuQSU4LUBRdcAMQSL9LdKk6bk4wRGSqJQBM42Fou7AaT66680LXknnznnXfcxn7llVcCfnHWPQQ3ASUGhdv0yR13wgknAN7tVFhY6Nyq4e9UBPpu/fr1nXzSWW08KkMKuq80T9WSTe5bzT3ds1y9F198MX379gUqvsDr9zXPr732Wg4++GDAu201r/RcSjOetdHoPa01MsL1/HbbbbcKn/ZRVFTEqlWrXEKPnme9evWcroWfW7jcRoYt+OQ94bLLLgN8glm6TiWRTH/99ZdbZzUHNZ923nlnwJOWoCx6ZmqrKWMnWI4DsaQ0nZCU7Caq9ffTTz91YQRtouHySJWArVy50oXUytpEtTZozK1JgsFgMBgMGUJSCUOyuAoLC51l06tXL8C7IcQYFZQeP368S6VXQotcvY0bNwZ802RZwZtssgm77LIL4C3gZJnn+vXrGThwIAC33HIL4FmBLC81Ebj88sud/LK0Dj/88BLXkyUULKwXA5AFJXaYKIKWrILdSgoZO3Ys4C11NXro2LGjc3nJHRNuCnHeeecBnnmm8yy+cMG+IKuvtEYb4e/KUhazUNLRwoULnWdD96DEjPIi3D7w9ddfd54RJftI1nCbuylTpriG74LmhhIqVPYkK7+wsNA1JJDbPBVu/Ugk4qxzlVV17doVgIsuugjw7PqPP/5wrSglp1zU0p1tttkG8A3Ma9as6Z5hRS12PU+VOaxevdqVzOgZh5t1BPVD4y+2rOblanEn6B7y8/MrrNtr167ls88+44wzzgBiDVMg1lBkxx13BPzcE/RbWt8ee+yxOI/OPvvsA8CwYcMAPybpKlXR+H3yySeuiYDQoUMHAPbee2+gdA+InoPCQjpdRZ4Jee06dOiQEq8g+HKUUaNGOZ3W3zQ+Gj/N0ZEjR5bpwdHYytOoeVFReY15GgwGg8GQIFLWGF67vaxnvYopKlFi0KBB/PXXX4CPG6q8JVgIDb5I/Zdffkk5KyooKHCF4IpXKZAulqD316xZ4+KyQ4cOBXBWZ1kJNllZWa7hgKz3ijKLYGKF4pVqUSb2KIa/7bbbArHn8cwzzwDeStS4y8pX7KosVphKyOpTPEQM57777gN8XKioqChunBTPFJMS41DS1uabb+68BUrqkadCcd3yItj2S7orZiHrXSUROqbphhtucDIpWUWJN/JmSLeF4uJi9zxSyTKKi4ud3AMGDCjx2/o9jVHr1q1dA3s1VFCik/RcjEnzLxUJZVorVCK1bNkyRo0aBcB///vfErKLlW+11VZATD/U/EBJiZ999pm7H/BF/7pGMjLXqVOH7t27O++Mrj19+nSXZBX2mmgeSW/r1avndEjxOM1f5Sj07t0bKBnHTyXE1ufOnevWNXlO1PBAeStKysnOznb3KHZ/4403Ap6Bq2REOrfZZpsl7UEJx1Gfe+45t35ofdPaquRTeXGWLl3q5l54DPV/JTdpHlR0rI15GgwGg8GQINJ+JFm4EcKmm27q/q2UaJVQyBqTpaiC7bVr17qszFSxo2g06iyc22+/HfAWlzJY1TTh4IMPdv5xZcxuTI5IJOJaR8kiTtQClkUrtjlmzBh3LcUeFFsOl8pAPOsXwgcfZ6JdYrgYXIxZcSqlnmdnZ7t7VBq/WKXi6WeeeSbgy4bE9oLQPR577LEJyRksHxEbkPWtchQ9D5UdrFixwsVcxo0bB3jLPJxBHjw2S1mwqRz/aDTqLOo777wTiGWLgz/uKpiJLCtdcTB9Vyw1HUdj6ZrylnTr1s3NdWWjKg9CzewVpy0uLnYZ94rVHXLIIYCP3Sv+prmQDItTAwy1qZPOvfrqq3FZq2Hsv//+ABx22GHOiybmKq+FyuMUu1Nz9lRDOta6dWuXWxJu5j558mTA50gccsghjqWqLEljKq+dYrcag1Toi2SVLg4dOtStVfKIhMuulJ+w9957uxKc8MEOum/FwjUPKlphYMzTYDAYDIYEkbHDsMMx0SDEAFWXKMjKAx9zSWUBrmRS/aMY8G677Qb4NmyNGzd21kkiVooyFCvK8CSfrPHjjjvOZf2JVW5IHv1uVWhar3sXizz33HMBP9Z6BllZWY6RifHpVQxT9yMmn8rGDmI1eXl5Lh44Y8YMwNeYKcame9pzzz0dY1DtmLJqVb8Y9hA0a9YsrvA+VdD1ZGlr3DT3guMVjtcptp8JSI6WLVu6VnGKEYv5ijWrKH/NmjUuDqpaVN2fdCvVzd+j0ahbf8TeO3Xq5NaLcN2voDre2rVru89ofFXPKran7HnF8OrUqZPSuKd+v0+fPi6nQ94fjbW8QrrHH374wbE0ZQ6rsb3iyWKtqfSe6FrK5L322mvjvGXhOS9v1Z133uk8Lp9++mmJ78gbpM8mHZtN6tsGg8FgMPwLkTHmuSGUxUqDFnk6m6vL0lFtWdifXtEDXpNlRPp9xRtq1Kjh2Eo6azLTifCzFnsIWu1lHT6dzoN2NdbK9B42bJhr36gsbDFgWeY6yPuSSy5xjCIc+9F9hY9eKy4uTrtHQOO4IVYgz4Ua1ivOlElvRVFRkRsnsTXNRbFMdb+B+IzUdByRVhaCvyEZy4LGfe3ate7+lDshFiT2KpYkj0Wq1ztdLzc3lwMPPBDwbFKHoyvrVke6rVq1ysmlbGd5CMT207kOBfsIbAzSgdatW7uchLA+aO0Md62qKIx5GgwGg8GQIKoE8ywLmTjKK4iqFCMMItjAOBPWdSZRVRh0uJPN0KFDXXavOuGoNlVxTMWI1q9fXyYr3lCsvypA9617CbP9TCHMIqsDyitr0KsSZlHyYqgWPF0HMwjFxcVuPTnmmGMA3yBeNajqd1xYWOgy9dW5LN09eJNFcJ6JxQup1u0qvXkaYsj0QvZvRnAR10KhBuPhFoxa6P4JzycT5UqGeFSGwS69lXGoE17CG3c0GnXNHRR2qKpGYGnQvAyfVJOq+WpuW4PBYDAYEoQxT4Ohn7uP3wAAIABJREFUFATLE8JHX6XbtWYwpBNhRqbSjdLaRFb1sEN5oJaTCrso8S9ZBmrM02AwGAyGBGHM02DYCCweaPgn4p/AKssDMc1UN9035mkwGAwGQ4KIJLILRyKR5cCS9IlTIbSKRqPxncH/HyZzyrBBmaF6yl0dZYbqKbfJnDKYfmQOZcqc0OZpMBgMBoPB3LYGg8FgMCQM2zwNBoPBYEgQtnkaDAaDwZAgbPM0GAwGgyFB2OZpMBgMBkOCSKhJQpMmTaL5+fnpkqVCmD9//ooNpT83bty4ysm8YMGCDcpcHccZqqfc1VE/oHqOtcmcGvxT52KTJk2irVq1yqRIG8W8efPKlDmhzTM/P5+33norNVKlCHXr1t1gXVB+fj6zZs3KlDjlQsOGDTcqc3UbZ6iecufn57tTJaoKGjRoUK6xfvPNNzMhTrlRr169jY7122+/nSlxyoU6depsVOY33ngjU+KUC/Xr1y+XflQ3uVu1alXl9KN27dplymzt+QwGg8FQLug4PrW60zFf/8YWlhbzNBgMBoMhQRjzNBgMBkOpCB8Av3LlSgB+/vlnAFq0aAHgDs1ev379P+Jw+PLAmKfBYDAYDAnCmKfBkCQikYiz0AU7MNtQ3ZGdnc2SJbF8mfnz5wPwyCOPAPC///0PgEsuuQSAM844A4CGDRtmWsxKg22e5UAkEok7ZT0cMK8qrgrJFYlEXBC/qshWXmisSzvZPgjdV6bvT3IFXVkvvfQSALVq1QKgf//+ANSoUSOjsiWCSCRCbm5uqX+TXuu1shBOUIlGoxU6f1Lf1/XMuImH9Fo6O2vWLC677DIAt4n+8ccfAGyyySYAPPTQQwAuS/bKK69kt912A2DdunVpk1XPM5FEJa0TwTUy0WuUkKFC3zIYDAaD4V+MSmGe2vHD1kNVYUiSSyyiuLiYv//+u8Rnfv31VwA222wzwFvolXUquxjE2rVrAfjzzz+pX79+ib/J2t4Yo6tMBFn+xizXMJvIFOSiffHFFwEYO3Ys8+bNA7weXHTRRQBceumlABQUFGRUxg1B47Zu3To+/PBDIN76ViJI06ZNgcwzUMn48ccfA/D1118DsMMOO7D55psD5dfjnJwcx5hWrFgBwBZbbJFSeaszNI5aJ5599lkARo8e7ca/Tp06gF/vtP5pXZw9ezYAzzzzDDvuuGOJ66WyjEVzb82aNYBfo8sD6fArr7wCQPfu3YGYq7kie48xT4PBYDAYEkTGmKesm5ycHGetfPfddwC0bNkS8L72TDHQcOxKVs2qVasAuP/++wF4+eWXWbRoUQkZf/zxRwD+85//AHDttdcCsc4ekH6mUVp8AnwMYvHixWy11VYAXHDBBQDu/5XBjiVvWc9WTCM3N5cXXngBgMcee6zU7+haiiueeOKJGWF2Gutp06YBMHToUAB+++03x/J///13AF577TUATjnlFADy8vKAyvGuhJn5b7/9BsCDDz7IXXfdVep3dt11VwBuuOEGwDO1dDNQzUGxlgkTJgB+Lh522GHceeedJT6rMQ17tHSNzz//nJtvvhnwDPbuu+9OWtZgHDb4/9JQXu9acE1Kdz6FfqtmzZoAPP3004D3lvz4449Or0899VQgxvwBRo4cCfjx1LNYuXKl83CVFU9PRtYHHngA8Oxxzz33LCFfQUFBmR4JsVQlP3377bcAnHXWWW5PSsQrZ8zTYDAYDIYEkXbmKWtMlsnrr7/urFlZ6U899RQAzZs3BzLDjGrWrOkscmWSience++9QCxuCHDQQQex7777AvDVV18BULt2bQD++9//AtClSxcA3n33XQDatWuXFis9nOUrWe+44w4AdtppJwAGDx7MaaedBsDWW28NQKdOnYDMMc+gt6Gs7EaxuS+//BKARx99lHvuuafEZxR3E7vU83r//feB2FinI8MvKD/EM87ly5cDMXYmVj9kyBAgxvwBfvrpJwAaN24MZGbsw3KLaU6fPh2AG2+8EYhZ3rLGNcaak2L/0p3hw4enXW7wTEbMXQxDcc6WLVvGMemwV0Oeo0cffRSA22+/3d2XPrts2bIKyRf0+Egf9d7q1auB+BhfJBKhQYMGJWQMrw1iaZ9++ikAzz//vCv/UGZrKmKHWVlZcRnMYpwXXngh4L1q22yzjYvdH3TQQYCfX+PHjwf8vBUaNWqUMsapsapZsyZz584F4Oqrrwb88/vkk08A2H333YHYWlDWHNNz6tChAwC33XYbEGOvW265JZBYFrYxT4PBYDAYEkTKmGe4dkZWr6wAxeJGjBgRZ/XJYiurvi8nJ8dZIRW13CWf/PvvvvsuDz/8MADPPfccELO0AEaNGgXAIYccAsRY5pgxYwCYOHEiAEceeSTgLeTWrVsDngmOGTMmLkM3FdA4XHPNNUAsuw1i1jXA3nvvDcRYmgqY//rrrxLfTTf0/GRdT5s2zVneiqXpeYgRyAp86KGH2GuvvQC4+OKLAdhjjz0AryeXX3454Nn2xIkT6datG+Cfb7JWeiQScax48uTJAJx33nmA90goNnTUUUfxww8/lLgv3Xs4kzH493R4JoJ1pTNnzgT82Or0GMkycOBAjj32WMB7TuQFUn2frjFs2DB3/VTrUSQScTqqHAKNm3IJBg0aBFCiGYU+owzzJ598EvBz9IMPPgCgffv2TpeUX9G1a9eEZQSvV3PnznVrmp6jWtaFUVBQ4H7vhBNOADyjLysDfvLkyW79UeOBZHRaevfrr786xjxjxgwArr/+esCPrbxXu+22GwcffHCJ72tNC+uuYqPBLOZk9UR6umTJEiej5p5+5/vvvwdg0qRJwIY9JJJZ97d06VIgtuZcd911wMZzM4Iw5mkwGAwGQ4JICfPMzs52dT+K8ag+6J133gG8RXvUUUfx+OOPAyV92uAtDb2vWp633nrLfUaxrUSssKysLGfZio098sgjNGnSBPAs7rjjjgN8TZPkGD16tPuMfP2yHMWoxI7Utmrs2LHllq+8qFGjhssSlKUlVjFgwADAW7LLly93VqLGrqxMMlmVwXiIGH5F2FG4TvOBBx5wWXH9+vUDPOOUpajasqOPPtrF5PR89Ox0H2eddRbgY3jPP/+8Yxbt2rUDkuga8v9jsWrVKsc45YlQ3FIZtMpirl27tovDhq8jNqK4khprd+rUie222w5ILisx/Ewfeugh1+3ovffeA3CsWOxHY967d2823TR2zq+ee7NmzUrILy9Rur0WGoP27dsDfh2RF6Ju3bpATB/FrqUXV111FeBzFuShOPHEE4HYmtOzZ0/Aj1ei2dkan2+++QaIMXNd85dffgHgpJNOAvz6IXzzzTecc845AM5Domeh+apXvd+hQ4e4OG0yEKv84osvXM7JggULAM/mlBGuNXbIkCFuHkkGPRfVB+u6Yv8rVqyI+06iuhP2XD388MNMnToViOksQK9evQDvcdM5wr/88ouLj4efseRQrarm3/jx4xk8eDAAbdq0Acrn4Uxq89TALV682CVKqFhWyT+dO3cGYgscQNu2bV36uSaGkhV0eKuSBLRBbLLJJvTp0wfwgeHyLo5ZWVnUqVOHESNGALiH8Oijj7oNL9xEQK8qpRkxYoRLYpEbI5yYIuXRSejpWGxycnKcm/bMM88EfCBfC4nuZeHCha7QXclOGrNwOYAm6bJly9w965l07NgxYTmDLiKILeJ9+/YF/EIuN4lc5prQxxxzjJMvHLzXZJLyN2rUyF0zVeOtRfLbb791BpASbo444gjAJ3Dceuut7jtaVIJNKgBOPvlkwC/ompT169d3yRhnn312ib8lAj1DGVWjRo1yi7kWGLlcVdqjDWr9+vVOb1599VXAJ8DpGep+lCjXpUuXlLubo9GoS8DThic3neZZcEHVQvnEE08AsZIb8K48udf1WqNGDadLFdUTjYd0oVatWs6lrPGQ3obDT2vXrnWyikzsv//+QPxGq/mXk5OTUnetmkQ88MADLtSkZLFwy0KFr1q1auX0Q9eR8aBxkCGjsd99993dCSsVTd4LbvQQ0wVdX4aSEvRkQGvvGDZsmAvnaA3TvNJ1pT8yLteuXVshnTa3rcFgMBgMCSIp5imrd8GCBS41/+ijjwZwNFjlEbJGPvroI2fhiEHIUpD1LItIVvvAgQNdQkOi7pZoNMratWs55phjAJ+OnZeX5+QIX1PWlBIPunfvzqGHHgp4RhFmVypRUTF2OhpPR6NRZ42q0FcBc42lrNQXXnjBpV9r7OQGX7hwYYlXJQ78/vvvzjUqBrDtttsmLGc4kePXX391rnqVQGi8xLr0e+vXry83A9PnBg4cGNcmsaLQNdu3b+/cx3rWn3/+OeDdnkE5w6EHWfOykOV2lFt0jz32YPvtt6+wzEpoUvmMyjK6du3qWL68JErNFxPQa506dZgzZw7g56sYhax0uZ1VnD5u3Li0JMJpvOQt0e9rLoq5jxs3zrFSvdejRw/AF+7r/nWfqZiLmldyc69YscI1QxfDl76HkZOTw5VXXgng3LdKBpLHTi5TeWB23XVX2rZtC6S2MUVxcXHcGZ1a/wYOHAh4Vvz333/HleEoSSrcGlNy9+/fP+lyMY215kynTp3c+hsuSTv//PMBOPfcc4HY+qI1+qijjgJ8iE0JQtITlTT16tWrQk1MjHkaDAaDwZAgkmKesrT69evn2sPJMpPVIKtPlsrs2bOdpaOYpgK8sm4VNA+2BKto+zUdYSTrQ1ZNadcLJouAjwOddtppLiajGIDuT4kuel+lIukohl+3bp2zmoJt+MAn14iBPPzww+6eb7nlFsD7+lXcr3j0gQceCMRabykpJpm4hSxlsYjjjz/enQMohqYSCXkCytO+TFauShB076eeeqqLf+o5VBRBq1dJWGI/ui8lhigG+sknn7jibcWWlMgga16y6/4bNGjgxla6kkhiiM4QVdKHYvo9evRwz07X05iE21EuXLjQldso7h0uV1DpiBIp0nWUl5671hS96llrrZg8ebJbL5Tgp6YVKkMpiwEmAz175TRceOGFblw3NteLioocG1bOgjxUSkCUx2KXXXYBYkwq2SOzID5W+/bbb8ddV0l2SoCT56+wsDCuGYwak4TZsNqSpiL3QNfWmvbEE084z1I4fnn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      "text/plain": [
       "<Figure size 576x576 with 100 Axes>"
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     "metadata": {},
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   ],
   "source": [
    "plot_100_image(data['X'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def segmoid(z):\n",
    "    # z = theta 与 X 向量的乘积\n",
    "    return 1/(1+np.exp(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost_reg(theta, X, y, l=1): # l为正则化参数\n",
    "    # theta (401,)\n",
    "    # X (5000,401)  第一列全为1\n",
    "    # y (5000,1)\n",
    "    reg = theta[1:]\n",
    "    h = segmoid(X @ theta)\n",
    "    assert h.shape==(5000,), 'error : h.shape {}'.format(h.shape)\n",
    "    m = len(X)\n",
    "    reg = (l/(2*m)) * (reg @ reg)\n",
    "\n",
    "    first = y * np.log(h)\n",
    "    second = (1-y) * np.log(1-h)\n",
    "    \n",
    "    return np.mean(-first-second) + reg\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gredient_reg(theta, X, y, l=1): #不需要学习率，自动调参\n",
    "     # theta (n,1)\n",
    "    # X (m,n)\n",
    "    # y (m,1)\n",
    "    m = X.shape[0]\n",
    "    reg = (l/m) * theta\n",
    "    reg[0] = 0\n",
    "    h = segmoid(X @ theta)\n",
    "\n",
    "    return (1/m) * X.T @ (h-y) + reg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def one_vs_all(X,y,l,k): # 其中k为分类的标签数\n",
    "    # X 的第一列为 1 (偏置量)\n",
    "    all_theta = np.zeros((10,X.shape[1]))  #(10,401)\n",
    "\n",
    "    #对每个标签都进行一次筛选，符合当前循环标签的y_i为1，不符合的其他9个标签，y_i为0.abs\n",
    "    #将上述操作重复10次，即可得到每个标签对应的theta矩阵(10,401)\n",
    "\n",
    "    for i in range(1,k+1):\n",
    "        theta = np.zeros(X.shape[1])\n",
    "        y_i = np.array([1 if current_y==i else 0 for current_y in y])\n",
    "\n",
    "        result = minimize(fun=cost_reg, x0=theta, args=(X,y_i,l), method='TNC', jac=gredient_reg, options={'disp':True})\n",
    "        \n",
    "        all_theta[i-1,:] = result.x # x：优化问题的目标数组\n",
    "    \n",
    "    return all_theta # (10,401)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predicte_all(theta, X, y):\n",
    "    #X (5000,401)\n",
    "    #y (5000,1)\n",
    "    #theta (10,401)\n",
    "    h = segmoid(X @ theta.T)  #(5000,10)\n",
    "    predict_y = np.argmax(h,axis=1) + 1# 沿着1维轴，找到最大的值，并放回其索引\n",
    "    predict_y = predict_y.reshape(5000,1)\n",
    "    assert predict_y.shape == y.shape,'error: predict_y.shape {} != y.shape {}'.format(predict_y.shape,y.shape)\n",
    "    num = predict_y==y\n",
    "    return np.mean(num)\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
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   },
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    {
     "data": {
      "text/plain": [
       "array([[-2.38188908e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "         1.30443134e-03, -7.55425169e-10,  0.00000000e+00],\n",
       "       [-3.18445549e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "         4.45835773e-03, -5.08291074e-04,  0.00000000e+00],\n",
       "       [-4.79316194e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "        -2.86536335e-05, -2.47190356e-07,  0.00000000e+00],\n",
       "       ...,\n",
       "       [-7.98537313e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "        -8.96500267e-05,  7.22279259e-06,  0.00000000e+00],\n",
       "       [-4.57051321e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "        -1.33737557e-03,  9.99743778e-05,  0.00000000e+00],\n",
       "       [-5.40406888e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "        -1.16585669e-04,  7.86711703e-06,  0.00000000e+00]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.append(np.ones((data['X'].shape[0],1)), data['X'], axis=1)\n",
    "finall_theta = one_vs_all(X,data['y'],1,10)\n",
    "finall_theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'accurate = 94.46%'"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accurate ='accurate = {}%'.format(predicte_all(finall_theta,X,data['y'])*100)\n",
    "accurate"
   ]
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